Thanks!!! That must have been the problem. I wanted to make sure I had installed it forge and everything else correctly, so I scraped my server completely and re-downloaded the files.
Here's what I did to find out which mods were client side mods:
ROUND 1:
I added the mods in one by one. If they had block ID conflicts I would change them until it fixed that problem, but if it crashed the server for reasons other than block ID conflicts, I deleted the mod, then moved on to the next mod (Repeating this process for all 154 files).
ROUND 2:
After that I went back through again and tried installing the mods that crashed the server previously. I did this because I wasn't sure if the mods that didn't work were dependent on another mod (Like a core mod or something). That fixed about 50% of the mods that didn't work.
ROUND 3:
For the remaining mods that didn't work, I made sure I had the most up to date version of it and tried installing it again. This fixed about 50% of the mods that still didn't work after round 2.
ROUND 4:
Now that I have done everything I can (or at least that I am aware of), I can confidently say that the remaining mods are client side mods.
FINISHED
Runs like a charm. 4 hours of work, but it was worth it. Thanks for your help though! Without you I would have never known about client side mods. I understand them now, and by process of elimination I was able to eliminate them! Thanks TwoTails! Your help is greatly appreciated. I hope you have a great day!