How to use Enkidu

well he has 3 quicks with high hit counts and decent star generation, so he is a good crit stat generator (at the least a secondary one) his best teammates would probably Skadi (JP) or like Hans, and then a Crit unit.
You could also pair him with a Merlin, as a Merlin with his NP and a Enkidu throwing in like a quick would generate a large amount of crit stars, and allows Enkidu to use Merlin’s buster up and his own to do fairly insane amounts of damage with his NP, you should probably still have an actually buster crit unit (Jalter/Musashi, etc)
And lastly you could pair him with Mash and Merlin for a good stall team that isn’t “arts” (basically is)
The 1st team comp is the most orthodox and probably the cheapest to build
Just know that he isn’t a damage dealer, he has low attack and a defensive kit, so supplement him with a damage dealer (preferably one that shines with crit)

Enkidu's main source of damage is from his NP. Having the 3rd highest damaging NP among all lancers as well as a very good hit counts and NP gen allows him to be able to be a main source of damage. His best teammates I'd say is Osakabehime (JP). After strengthening, Osakabehime's NP also grants a buster buff alongside quick buff which is perfect for units like Carmilla and Enkidu. For now, you could pair Enkidu with either a quick support or a buster support. Use quick support if you want to increase his basic attack damage, use buster support if you want to increase his NP damage. Unfortunately you can't make a very optimal team with Enkidu for now.

You are exactly right in that Enkidu doesn't mesh well with other comps. My personal preference is to pair him with Hans and Kotarou to give him a bit of support and survivability. The sad thing about Enkidu is that it doesn't really have anything it's good at doing except stunning divine enemies and having a really big self heal.

I my opinion, I prefer to wisely utilize his ability for star generation+NP damage. Then rely on critical A-QQ or critical art as 3rd position to make his NP spam as fast as possible. Any good supports with 2030 to make a critical team is decent for him.

Besides, there isnt too much good idea to make Enkidu in a team.