When a runner is called out after a play for missing a base (see Rule 14.02l) or failing to tag up (see Rule 14.02m), and that is the 3rd out of an inning, does the call nullify any runs that scored on the play?

These outs are applied as of the end of the play, therefore:

On failed tag-ups: the run is nullified only if it was the scoring runner that failed to tag up.
On missed bases: the run is nullified only if it was the scoring runner that missed a base, OR if the runner that missed the base was in a force situation compelling them to reach the missed base. [Example: if a kicker never touches first base, no runners on base may score (see Rule 10.09).