7-high as in no straights, pairs, or flushes? Just look at the number of combos:
For 7 high:
4 combos (2-3-4-5-7, 2-3-4-6-7, 2-3-5-6-7, 2-4-5-6-7)
In each combo each of the 5 can be any suit so 4*4^5
Then we have to take out flushes, 4 for each combo, so 4*4^5 - 4*4 = 4080
I just did this right now so I could have missed something, but I think that's right.
The other ones are tougher, biggest thing is just finding how many combos there can be for like K high without making a straight. Or maybe you could just find total combos and subtract out straights like I did with flushes.