Did you try to bash the door? As i remember all the doors in orc cave you can just bash them :) no key needed

Well yeah, I have tried. But those doors got tons of hp. So I guessed it was impossible. I guess I can give it one more shot!

Alternatively, you can also try to get points in Pagan magic up to Student level, and then learn and keep casting the spell Shatter until the door opens as even a door with 1000 hp will open with a successful spellcast. (One of the most useful spells to learn as early as possible) It doesn't damage your weapon to force you to return to town or call genie for repairs and mana can be replenished fairly easily.

I was in the same situation and I ended up taking down the goddamned doors with my weapons. I spent 1 or 2 hours searching for keys in the caves´s three levels while I keep pressed down alt the whole time. Never found any key : /

Have you already see my map?
link

In the map above, you can see that doors F1 and F2 have a key, the other 4 doors don't. So, you must destroy those to go further. You can use your melee weapons, but I suggest to you arrows (since they ALWAYS hit the door) or your seals, if you saved some - seals always hit too, and are more powerful.

In this sense, Shatter spell is very useful - it opens any (it depends on the level of the correspondent magical discipline) locked door or chest with no time loss.