You will not be able to re-enter Israel on your expired student visa, but you can obtain an ordinary tourist visa (B/2) on arrival, which will be good for up to 90 days. If you can narrow your time to a few days, you might be issued a transit visa on arrival instead.
Provided you have not violated the terms of your student visa and meet the usual requirements (demonstrate onward transportation, have at least 6 months validity on your passport, and possess adequate funds to cover your expenses during the visit), you should not need to make any special arrangements before your departure from Poland.
As always, it's best to double-check with the Israeli embassy or consulate most convenient to you, as rules may change from time to time. But I'd venture that holding a U.S. passport is perhaps second only to an Israeli one for ease of travel to or through Israel.