There are several recycling points and wasteyards in Szeged. At the recycling points you can find containers for paper, plastic, white and coloured glass, as well as aluminium. At wasteyards you can also dispose of dangerous garbage, e.g. batteries, electronic devices, refrigerators, etc.
Check out this site for a map of all wasteyards and recycling points in the city: http://szegedihulladek.hu (scroll down a little, the map is under "Hulladékudvarok")
If you want to dispose of used cooking oil, take them to MOL gas stations. You can find a map of all MOL stations in the city by searching for 'Szeged' on MOL's website: http://toltoallomaskereso.mol.hu/en