> Question: 
>
> What is Israel's strategy in invading the Gaza strip?

There is no good strategy for Israel in invading Gaza.  It's a tactical punitive move to try to impose a significant cost on Hamas.  Israel cannot permit Hamas to strike it with impunity, much less on this scale.  This is the only motivation which an invasion of Gaza addresses.  

Israel doesn't want to occupy Gaza.  They directly occupied Gaza for decades after the 67 war and withdrew unilaterally from the interior as a tactic to reduce their own casualties.  Gaza is one of the most densely populated areas of the world with about 2.4 million people. The IDF would struggle to pacify Gaza.

Israel is also unlikely to convince Egypt to accept responsibility for Gaza or it's refugees.   Israel has tried to give Gaza to Egypt as part of the Camp David accords which saw Sinai Peninsula repatriated to Egypt.  Egypt wouldn't take it.  Their position is the refugee's in Gaza are of Israel's making and Israel's responsibility.