What are the viewpoints and policy positions of the Israeli right wing?
TL;DR: Just as in USA (or elsewhere), the whole idea of "right wing" and "left wing" is a ridiculous oversimplification that is not very well suited as a good way to model political clusterings. There are very few coherent unified "right wing" policy positions and viewpoints, other than general average opposition to things on the "left wing". However, there's some correlation to economic views, cultural views, religiosity and geopolitics (the latter includes Israeli-Palestinian situation).
The problem with analyzing Israel's political situation is that it has complications. Lots of them.
Insufficiency of a single-axis political spectrum to model modern political life (as opposed to multi-axis models).
This isn't Israel specific, but is actually amplified as a problem by subsequent points.
As the old Russian Jewish joke goes, "Two Jews - means there'll be three opinions". Israel has multitude of parties, many of which are single-issue parties, some of which don't neatly (or at all) align on 2-axis left-right spectrum.
Within larger parties, there are blocks which aren't always of the same mind.
Plus, the parties aren't necessarily stable, budding off new ones from larger ones all the time - sometimes based on policy, sometimes because a party bigwig is jockeying for more power in a different party, after not getting enough influence in their own. Anytime I observe party politics in Israel, I'm reminded of David Duchovny's film "Evolution" and its alien ever-shifting biosystem.
Israeli politics is frequently built around personalities, as alluded to in last bullet.
For example, witness what happened when Ariel Sharon left Lukud as a classic example.
Israel has its own set of idiosyncratic political issues.
Religion vs secular side; Israeli-Palestinian relations; religious and ethnic groupings (Jews, Muslims, Christians, Druze, Ba'hai; Jews/Arabs/Bedouin). As if inter-confessional politics wasn't complicated enough, just Jews itself have Sephardi-Ashkenazim main divide, with Ethiopian Jews and a bunch of smaller demographics thrown in for flavor - overlayed with Soviet Jewish immigration and the issues embedded therein; and Christians have Orthodox, Roman Catholics, Armenians and I'm probably forgetting others.
So, are there at least some rough correlations that can be considered aligned with left-right axis? Yes, to an extent. With all the complications and caveats mentioned above.
As is generally the case in many Western societies, some groups that are considered right-wing typically favor slightly more emphasis on private sector economy, slightly less government intervention, slightly less government spending.
A caveat here is that Israel is generally very economically left country on average compared to USA (the founders were almost invariably all socialist/communist. Heck, this is the only country that reliably and on somewhat larger scale managed to actually establish almost fully communist polities - kibbutzes). As such, "right wing" economic views in Israel are likely to be center or center-right ones in USA. Policy by policy, I suspect there isn't all THAT much meaningful difference between economic approaches espoused by Netanyahu and Obama, but exploring that is not going to fit into the margins of this specific Q&A.
Another caveat is that there are parties that are considered quite "right wing" but whose only economic program is "gimme more money from Treasury for my constituency". Shas (constituency: religious Sephardim) seems a perfect example.
Within Judaism, there seems to be a correlation whereas strongly religious parties are considered "right wing" (this is a Jewish-only thing. Strongly religious Muslim/Arab parties are reliably left wing, including on things that are not directly related to Israeli-Palestinian conflict. And yes, for the "Israel is 'apartheid'" crowd out there - Knesset has not one but several Arab/Muslim political parties).
However, this is mostly correlated on cultural angles, and less so on economic ones.
Of course, it wouldn't be Israel if things weren't messy and untidy in politics. Aside from Muslim religious parties being left wing, Lieberman's "Our House - Israel" party is considered strongly right wing (probably more so than Likud) - and yet, is probably more secularist and anti-religious-influence-in-government than most left wing parties. Its major policy planks are things that are anathema to samesaid strongly religious parties - busses and stores working on Shabbat, Yeshiva students serving in the Army, etc...
There is a school of political thought which tends to analyze much of political dynamics in Western world through the lens of what's called court/country, or cosmopolitanism/traditionalism, divide. It's generally very useful when trying to analyze populist movements.
There is an important but often overlooked divide that runs throughout modern western history (possibly other histories as well; I’m not familiar enough to say) – a divide between what we might call cultural cosmopolitanism and cultural traditionalism (the more loaded term is modernism v. anti-modernism). You can see it in studies of Stuart and early Hanoverian England, where discussions of so-called court/country disputes are central. You see it in various populist insurgencies throughout American history. It features prominently in the works of American cultural critics, especially the late Christopher Lasch.
As such, Israeli right wing is typically - as in the rest of Western democracies - associated with the "country" and "traditional" cultural side, whereas the left with court/cosmopolitan.
A lot of cultural issues can effectively be analyzed this way. Strongly religious parties tend to be on traditional side, and are right wing (but see above - being secularist isn't a left wing thing, see Lieberman's I.B.). Socially liberal issues (LGBT rights, secularism) are mostly clustered around cosmopolitan views and this more of a left wing thing.
Geopolitics/ Israeli-Palestinian conflict
Mainline/centrist views aren't all that dissimilar on right and left here. Both sides generally (again, among mainline) support 2-state solution, eventual Palestinian statehood, negotiated agreements, and - as a concept "land for peace" approach. Both sides mainline generally oppose things that are detrimental to Israel's survival (right of return).
Where two sides differ are three aspects:
The extremes are generally clearly congregated on one axis. Nearly all opponents of 2-state solution and perpetual occupation are on the extreme right wing. They aren't mainline right wing, but you won't find that point of view on left wing at all. Similarly, Israel-damaging views are congregated on extreme left wing (ranging from supporters of right of return, to people who consider Palestinian refugee issue to be Israel's fault, even though Israel didn't actually expel any but a very small minority).
Of course, this wouldn't be Israel if there wasn't a weirdness and reversals. Strongly religious parties are typically considered very right wing. Enter Naturei Karta (and smaller ones like Edah HaChareidis) who are so religious, they consider modern state of Israel an illegitimate state that shouldn't exist, because it wasn't created by Messiah. Yes, they officially and openly root for destruction of Israel, and are buddy buddy with Iran.
Right wing tends to be FAR FAR more cynical about goodwill of Palestinian/Arab/Muslim side in any dialog/negotiations agreements.
As such, they for example support land for peace in concept. But they look and say "OK, we gave Gaza land to Palestinians. Instead of peace, we got a terrorist state that tries to make war on us non-stop and whose founding charter calls for Israel's destruction. That ain't 'peace' which was the bargain we entered into". So, next time some land for peace deal is discussed, they become very skeptical, not of the idea but of the trustworthiness of the deal.
As is 100% typical and predictable if you use cosmopolitan/traditionalist divide, anything that smacks of "rights of the oppressed minorities" (which in Israel are of course Palestinian Arabs, for most part) tends to be a big priority to the cosmopolitan side. That's not to say majority of traditionalist/right wing side likes oppressing, but the issues around that are typically less of a priority in traditionalist mindset.