That's a good question.
There are those who say that the Gaza-based Hamas didn't plan this, that it was planned by Kaled Meshaal in Damascus and carried out by some partisans. Why would he do it? Maybe because he didn't like the steps that the Gaza Hamas was taking to form a "unity government" with the PLO/Fatah. So he ordered this attack knowing that it would put the local Hamas in a bind.
Now the local Hamas does not want to reveal that it is not in control of itself, that outsiders from Damascus can control actions taken in their name. So from that point of view, they had to take responsibility. Furthermore, Hamas has very few friends, and does not want to risk alienating Meshaal who has been helping them smuggle in weapons and cash. And Meshaal does not want to lose his influence. He gains by having Hamas ostracized, so he does not want to see the Gaza Hamas make a deal with Fatah that would mean ending conflict with Israel and resuming EU/US aid to the PA.
Another factor to consider is how Hamas has conducted its PR this last year. Hamas claims that its fighting is what caused Israel to leave Gaza. In part that is how they won the election. They have also claimed this kidnapping as a victory. So they cannot go backwards. Releasing him would cause them to lose a lot of face both inside Gaza and with Damascus and Tehran.
They don't have many choices. They could either lose a lot of face, accept the quartet demands and make a deal with the PLO (which they sort of did already, though not a good one and one that caused Meshaal to react), or they can bunker down and fight like Meshaal wants them to. Looks like they have chosen the latter.
....My question is this-what was Hamas's strategy in going into Israel and capturing a soldier?.....
They did not realize that the weight of an added straw would break the camel's back.
IMHO