Yes, they definitely can be modded. You can edit hex on any PS2 game and zip it in a PS2 ISO, burn it and play it on a modded PS2. There are PS2 internal modchips, but Action Replay is a cheap alternative. (you can also use Action Replay codes which are basically just on-the-fly hex edits on your RAM)
And most 3d models and textures can be editted with basic programs like 3ds and Photoshop.
Well it actually depends on what type of mods you are trying to do, and on what games you are trying to mod, but most likely I am going to say you can't mod too many of those games being they are so old. If you really wanted to I am sure you can find a program to mod a game or two, if you wanted to mod a ps2 system that is like the outer cover you can get parts for that through extreme-mods.com. On another note if you need any type of help for mods for your 360 you can let me know cause I do a few things for them my GT is DRUNK3NP3NGU1NS feel free to message me.