TLDR
This answer cites war goals, announced by Netanyahu himself, about the Gaza operations: 1. deterrence, 3. eliminating the planners of 10/7, including Sinwar 3b. getting the hostages back, 4. removing Hamas from power, 5. destroy Hamas troops 6. maintaining an Israeli security presence.
Until those goals are downgraded, adjusted or negotiated away, this answer is that the strategy is to exit once enough of these goals have been achieved. A number of them have not and Netanyahu's rightwing coalition partners are on the record that they would drop their support in case of an early departure.
Well, we can infer some of Netanyahu's war aims from his statements about the current war, past positions, observing Israeli actions and comparing them to past Israeli strategies. Additionally, while we cannot "read his mind", Israel is a democracy and Netanyahu doesn't carry the final word a la Putin. He is both constrained in what he can realistically enlist support for from other members of the Israeli polity and has to communicate to other politicians, which are externally observable.
A year into this war, it's not unreasonable to ask what the plans are. This answer will mostly concentrate on Gaza as it seems more problematic long term than Iran/Lebanon.
1. Deterrence
This is a frequent word in the Israeli press. The word speaks for itself, it is meant to convince, by force, Gazans not to attack Israel. At a guess, this is probably achieved, for the time being: Hamas will lay low, for a while, if Israel leaves.
2. No Palestinian state, ever.
That has been Netanyahu's long term position and there are no indications he's changed it. Even for a different Israeli leader, selling such a state to the electorate would be difficult after 10/7.
3. Kill Sinwar, and the other 10/7 planners.
Sinwar was killed soon after I posted this answer, but this goal had already mostly been achieved when I wrote it, with a number of other high ranking Hamas leaders eliminated. See also.
3B. Get the hostages back.
They have worked at it, but it's also clear some of the other goals have taken precedence, for example removing Hamas.
4. Dislodge Hamas from power in Gaza and/or get the population to revolt. Get more amenable Palestinian leaders.
There have been talks for example of boosting the power of Gaza clans and families. Hamas has been vigilant in rooting dissent out however.
Direct Netanyahu, April 2024
Netanyahu on Tuesday also repeated his oft-stated war goals of eliminating Hamas, returning the hostages and ensuring that Gaza never again poses a threat to Israel.
“There is a fourth objective: Hamas is part of Iran’s axis of evil, which aims to destroy us. And when we defeat Hamas, it is not only defeating Hamas–it is defeating the axis."
5. Destroy Hamas combat brigades
IIRC Hamas started out with about 10 combat brigades and Israel has tried hard to reduce them. That was one of the reasons to attack the Khan Younis area, 4-5 months back, as the last 3 or 4 were lodged there.
The trouble with this approach is that while the IDF can, and has, smashed any organized resistance at a given location, it cannot pin them in place, destroy them, and control the terrain durably. Look around press coverage and you will quickly see articles of the IDF redeploying to areas they had cleared before. The tunnels (pooh poohed by some earlier) are probably a big help there.
Direct Netanyahu, April 2024
“We will complete the elimination of Hamas’s battalions, including in Rafah. No force in the world will stop us…. After what [Hamas] has done, it will not do this again. Neither will it exist"
6. Establish durable security control in Gaza to prevent future arms buildups.
Netanyahu has talked about keeping an IDF presence. That tends to be badly received by the Americans who would prefer Fatah. Something Netanyahu emphatically refuses. Fatah, for itself, has expressed extreme aversion to coming in on behalf of Israel.
(Direct Netanyahu) "I think Israel will, for an indefinite period, have the overall security responsibility, because we have seen what happens when we don't have it.
More recently, Netanyahu has been talking up keeping control of the Philadelphi corridor (the Gaza-Egypt border).
7. Perhaps most importantly, biding for time.
A number of the preceding goals are still elusive at this point and the situation in Gaza is far from brilliant. And Netanyahu has so far failed to articulate exactly what he considers "good enough" to stop.
But staying in Gaza is not existentially problematic to the IDF in the short term (it is bumping up the deficit). If the food blockage claims didn't cause a rupture with the West, continued lower intensity operations likely won't. Maybe something will turn things around? Maybe the rest of the hostages will be recovered? And there is always the possibility of having a much friendlier Trump presidency next year.
Stopping in Gaza now would risk looking like weakness and confirming failure. His hard right allies have stated they would drop their support, thus collapsing his government. The more moderate want his scalp for allowing 10/7 in the first place. Stopping would also force looking at providing reconstruction for what after all remains an Israeli-controlled region. Last, it would leave a power vacuum that Hamas would fill right back up.
It's like teaching a horse to sing: maybe something will take a turn for the better.
(A bit of opinion, which does IMHO illustrate some dilemmas facing Israel)
After 10/7, a number of these points would be understandable (at least, if one doesn't look too closely at the 41000 Gazan dead so far).
However #2, no Palestinian state, ever, gives Gazans very little reason to eschew armed resistance. Yes, at some point they may cease fighting on this current round. But either Israel will have to maintain a police presence to keep the peace or they will eventually rearm.
Gazans are on the whole a very young population, living under very harsh conditions. They can't leave and nearly everyone has had people close to them killed. At least some young men will keep on getting killed while trying to kill their enemies.
So the deterrence aspect, long term, is questionable, unless Israel is even more coercive, which may result in ever-dropping Western backing. While it is not that surprising to see European criticism, even the US, especially amongst younger generations has seen unprecedented criticism. Will it happen? Unsure, but it is a long term risk.
Still, short term, it'll probably be a long while before Hamas really puts forward a strong attack if/when the IDF leaves.
Make no mistake: this isn't a standard guerrilla war. It's a stalemate. Given the current situation, Israelis can't "go home", like the US did in Nam and Afghanistan, the Soviet in Afghanistan or the French in Algeria. That's something Hamas doesn't seem to get: they give the Israelis as little way out as Netanyahu does to Gazans and West Bankers. That and Hamas are terrorists, not just "resistance fighters".
What is certain at this point is that both populations are suffering from policies pursued by the other side's government and that this looks unlikely to change unless major shifts happen in their goals.
Lebanon and Iran - a more traditional campaign
Lebanon and Iran however seem like they would be more manageable.
The Lebanese don't have nearly as much skin in the game as the Gazans, the country is nearly a failed state and Hezbollah's adventures may come to be unappreciated by Sunnis and Christians. The IDF and Hezbollah slugged it out in 2006 and Israel did establish deterrence. So far, 2024 has started out way better for the IDF, but it's early days and there are supposedly still a lot of missiles.
Iran, as long as it is non-nuclear, is 1000km away, and has no air force that can realistically threaten Israel, though its missile force has the capacity to inflict some level of deliberate civilian casualties on Israel (lessened by widespread availability of bomb shelters and Iran's reliance on mostly long-prep liquid-fuelled IRBMs). Its government may want to sit out a full out fight, as it itself has its own problems and has regional rivals. Israel could certainly hurt it, though that will also be limited by distance. In any case, unlike with Gaza and the West Bank and even Lebanon, in the domain of public sympathy, Israel is much more likely to get the benefit of the doubt from Western nations when targeting Iran.
There are risks: ground invasions in Lebanon can bog down, whacking Lebanon too hard can backfire wrt world opinion (especially if the methods to do so are controversial) and Iron Dome defenses are susceptible to saturation attacks and cost asymmetries (I find it hard to believe, but the number of 150k rockets, before October, was claimed for Hezbollah). Iran can also threaten to disrupt the oil trade and that's probably one of its better points of leverage.
But, while it is way too early to have much confidence, the idea of successful deterrence seems more achievable wrt Lebanon and Iran. The IDF is very good at fighting conventional wars.
p.s. "exit strategy", as opposed to "goals" or "aims" seems the wrong term. An exit strategy is not the goal a country goes to war with, it is a what you consider to be your minimum results allowing you to leave, after your initial goals have clearly failed. The US was looking for an exit strategy in Vietnam and Afghanistan. The USSR in Afghanistan. Israel from South Lebanon in the 80s. Russia (or Ukraine) may look for one in the future.
Talking about an "exit strategy" with regards to Lebanon is quite premature given that the war there is less than a month old. Israel isn't at that stage at this point, even in Gaza.