Kodak, Canon, or Nikon?

I need a camera for theatre and for filming something for a film festival… Which is the cheapest? Which has the best quality… And Which one can easily have the photos and videos accessed on to the web?

Kodak are worthless. If you're one of those fussy people who likes a camera to work, avoid them.

You're being a bit vague - if you're videoing a theatre performance, the brand doesn't matter. If you don't have permission, you won't get close enough. If you do, then the camera's capabilities are far more important than the name on the front.

If you're shooting your own video (film means, 'Not digital,' when referring to stills cameras - the distinction is very important) Nikon don't do camcorders, which are the best tool for what you want to do.

An intelligent person using a stills camera for video (if that's not a contradiction in terms) would probably go for a Sony SLT, but it's difficult to tell, because intelligent people know more than two manufacturers (Kodak don't count), and usually shoot video with camcorders.

I'm a nikon person, so I suggest that

It seems that your budget is way to low for what you want.

To shoot video, you really need a video camera and you can find good Full HD cameras with a 40x optical zoom. A camera like that should cost you under $300

Look at JVC, Panasonic, Sony and Canon camcorders as a start.

If you are planning on shooting still shots actors on the stage, you really need some kind of dSLR which performs well in low light and a fast lens (f/2.8 or faster).

Such a rig will cost you in excess of $3,000

What I have not mentioned are the skills you need to produce videos and brilliant stage still images. Those you can't buy

Canon and Nikon… Yes.
Kodak… NO!