This can be done by using a different, well-defined target selector for each case. By well-defined, I mean that every selector only works for one score/team combination, and also that it will only "look at" the player executing the killstreak.
The latter part is best covered by another score, which I'll call EXECUTE. I assume it will be 1 for the player executing right now and 0 for everyone else. How exactly this is determined/set depends on your activation mechanism.
I'll call the score to check SCORE and the team will be TEAM. You can then use the following target selector to target the executing player, if and only if his score is X and he is on TEAM:
E.g. to give the player a speed effect when he has a SCORE of 4 and executes his killstreak ability, you would use
/effect @a[score_EXECUTE_min=1,score_SCORE=4,score_SCORE_min=4,team=TEAM] 1 20
If the command you want to trigger does not use a target selector itself, such as
/summon, you have to
/execute on the triggering player using this target selector.