I did read the take down policies, but I was wondering if there are any conditions that would allow me to post these things. For example: Do I need permission from the original artist/OC owner to post new art of other peoples OCs or edits of other people's art?

Takedowns aside, "permission" is only really relevant in the event that the artist has a do-not-post status (conditional DNPs also exist, such as "no edits".) From avoid_posting's wiki page:

3. Special Permissions

If for some reason you have been given permission to upload something that is DNP, please include proof in the image description otherwise it will be treated as DNP content and taken down. This may include the rights being transferred, the artist giving you the right to upload or other rare circumstances.

lafcadio said:
Takedowns aside, "permission" is only really relevant in the event that the artist has a do-not-post status (conditional DNPs also exist, such as "no edits".) From avoid_posting's wiki page:

So does that mean I can post edits or art with OCs as long as it isn't listed as dnp or conditional dnp?

prototype-0 said:
So does that mean I can post edits or art with OCs as long as it isn't listed as dnp or unconditional dnp?

The site's rules do not prohibit the posting of artworks and edits, as long as they do not fall under the Avoid Posting criteria.

You are not required to ask for permissions from the artist or character owner, but I would highly insist on doing so first.
If you neglect on asking for permissions altogether, you run the risk of having the artworks taken down by the artist or character owner.
There have been many cases where artists ask to be listed as DNP specifically because people did not even bother to ask for their permissions in the first place.

you don't literally have to, but it's polite to ask