Can I cross the border from Ioannina Greece to Albania with my Greek ID card or do I need a passport?
Yes, it is possible to enter Albania with only a Greek ID, however you need to be sure that it is the new Greek ID which is with Latin letter.
Still a few older ones ID's are existing with only greek letters. With these you won't be allowed to enter in case of a border control.
EU citizens have been allowed into Albania with their national IDs since summer 2006
As stated by the Albanian MFA (page 1):
GRQIA: PASAPORTË & LETËRNJOFTIM
GREECE: PASSPORT OR ID CARD
However, in countries outside the EU/EFTA, such as Albania, only the new, bilingual card is a valid travel document.