How much can an iPhone 4 8 GB hold?

Would I have enough room for over 300 photos, 300 songs, 4 music videos all under 5 minutes and 10 seconds, and apps? Plus messages and 50 contacts?

It depends on the file size of all those files. All the files could vary so its hard to say

However, everything seems relatively small, so yes

I have over 4k pictures on mine and it takes up 3GB, and they are high quality, and roughly big pictures

Obviously 8 GBs, all depends on the size of your files.

Well you'd have to check as far as the pics, songs, music videos, since they all vary by size & depend on quality as well.
Same for the apps.

As far as the messages & contacts the iPhone has limitless storage for it.