To set a custom resolution go to \SteamApps\common\Jedi Outcast\GameData\base and open jk2config.cfg (WordPad will work just fine). Find (Ctrl + F on WordPad) seta r_customwidth and change both it and seta r_customheight to your desired resolution's respective width and height. Change seta r_mode to -1 and to get proper widescreen field of view add a line with seta cg_fov "95" for 16:9 resolutions or seta cg_fov "90" for 16:10 resolutions. It's important to point out you can experiment with these settings to find what best suits you.

Example:
seta r_customheight "768"
seta r_customwidth "1360"
seta r_fullscreen "1"
seta r_mode "-1"
seta cg_fov "95"

Note #1: for some reason attempting to play on 1366x768 will result on CTDs;
Note #2: your resolution won't show up on the video setup menu.

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Thanks to:
- pagb666 for initially pointing out the FOV issue.