Xbox-Scene.com - Xbox 360 Xbox360 Modchips Xecuter3 Xenium SmartXX X-Chip X-B.I.T Xecuter2.6 Xodus - Gamesave Dashboard exploit - EvolutionX Avalaunch MXM Dashboard UnleashX - X2 & EvoX bios - Copy Xbox Hacks & Cracks tutorials faq - Cheapmod
This was the hub of information on this stuff when I softmodded an Xbox a few years ago, so I can only assume it's still just as useful. (As an aside: Honestly, once you're done modding your console, do install XBMC as the replacement dash - it's pretty, it's useful and you can launch everything you could possibly want from it.)
The only PS game I bothered to play on my Xbox was FFVIII, which actually ran surprisingly well. Good framerates, perfect sound, no worries. I've heard compatibility isn't great, but considering the last time I dabbled in this stuff was 2006, I might be wrong now.
N64 emulation's OK - The emulator I used actually contained three different executables, and some games were more compatible with certain emulators than others. It's pretty much trial and error. The package is called Surreal64.
Here's a compatibility list. Last updated four years ago, but I'm not sure if the app itself is still being worked on.
Oh, and as for modding methods... The route I actually took was the font exploit trick, which did involve hotswapping two hard drives at one stage. On the plus side, you don't need to shell out money on a memory card and a game containing the save exploit - however, hotswapping the HDD is fucking tricky business, and does, obviously, involve opening the console.
Jam it back in, in the dark.