I've got three audio tracks of a Pro Wrestling event I shot tonight and the camera audio is 48khz 16bit while the Commentary audio is 44khz 16bit.

Will I have any issue syncing these up in post with the different khz? I usually try to always record the exact same settings, but I had to drop it to 44khz has it gave us extra time that we needed.

If you are using halfway decent software, it should be no issue at all. At least IME.
Note that it is frequently more advantageous to explicitly do the conversion than let it happen automatically. Again, this depends of what software you are using in your production flow (not revealed here).

You will need to convert the 44kHz file to 48kHz. You can't mix and match. Your NLE might do it automatically when you add the file to the timeline but for safety I'd do it as a separate operation, saving it as a new 48kHz file, and then using that new copy in your project to sync with the other files.

I agree with Steve. My NLE will handle the two bit rates within one project just fine; however, to ensure quality, I'd convert from 44.1 to 48 and listen to the result to ensure that it has the quality that you demand. If so, then you're set. If not, use a different/better conversion process.

I just ran into some problems while trying to move a project that had 44k files on Final Cut Pro over to Premiere Pro 48k project. But I think most products these days handle the conversion behind the scenes effortlessly; my issue was just an edge case.

Everywhere you look on forums and books you see admonitions about mixing 44k with 48k but I suspect most issues are software or user errors rather than an architectural problem with mixing the two.

I know of some golden eared music recording engineers who don't like the sound of digitally converting sample rates. They seriously play out of a high-end D/A into a high-end A/D and re-record the material.

For dialog, I wouldn't sweat it. Personally, I can't hear digital conversion artifacts with my tools.