Are your dice all (approximately) regular polyhedra? If so, then these are the 18 possibilities I think, expressed as number of d20s,d12,d8s,d4s:
4,1,0,6
4,0,2,5
3,3,0,5
3,2,2,4
3,1,4,3
3,0,6,2
2,5,0,4
2,4,2,3
2,3,4,2
2,2,6,1
2,1,8,0
1,7,0,3
1,6,2,2
1,5,4,1
1,4,6,0
0,9,0,2
0,8,2,1
0,7,4,0