Step 1: Go down the list to head to head.
1a: Eliminate A and D based on head to head.
Step 2: Go back to the top of the list. Go down to head to head.
2a: If either B or C has a head-to-head advantage, give that team the first wildcard.
2b: If neither team has a head-to-head advantage, (the series was split or the teams didn't play), go to total points. B makes the playoffs.
Step 3: Go back to the top of the list. Go down to head to head.
3a: if B made the playoffs in step 2, eliminate A for sure (because it's left with an 0-2 record against remaining teams). If C has a better record in this particular round-robin than D, it wins the playoff spot outright in this step. If not, once A is eliminated, you re-run the head-to-head comparison, and D earns the final playoff spot due to the direct head-to-head win over C.
3b: If C made the playoffs in step 2, compare head-to-head records of A, B, and D. If any team has a better record, put them in. If two teams have a better record than the third, eliminate the third and start back at the top of the list for the two-team tiebreaker. If all three teams have the same head-to-head record, A makes the playoffs due to the total points tiebreaker.
So, based on the information given, I see:
If C holds the head-to-head tiebreaker over B, then the teams that make the playoffs are C (as the 5 seed) and whichever team had the best round-robin record among A, B, and D. (If two teams are tied for the best round-robin record, then it's whichever team wins that two-team tiebreaker. If all teams have the same round-robin record, A makes it based on total points.)
If B holds the head-to-head tiebreaker over C *OR* if neither team holds the head-to-head tiebreaker over the other, then the teams that make the playoffs are B, (as the 5 seed), and C, (if it has a better round-robin record among the A/C/D troika than D does), or D, (if C and D are tied in round-robin record among the A/C/D troika).
Of course, this is all provided the information that you gave us if complete and accurate. The key is just to go back to the top of the list every time anything changes and work your way back down. When in doubt, go back to the top of the list.