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The 4 turtles vs. Sif and the Warriors 3. Standard weapons for all. Fight takes place in an abandoned NYC.

On the other side of a city another match takes place:

Splinter and Shredder vs. Loki and Heimdall. Splinter gets an unbreakable staff. Heimdall gets his greatsword and 2 knives. Loki gets his spear from Avengers but is limited to melee: no energy blasts and no illusions. He still has his daggers though. Shredder gets his full swiss-army-knife-looking arsenal.

First fight I would say the turtles. Based on throwing cargo containers around, tanking bullets and heavy impacts etc. they are in the same ballpark as the Asgardians in terms of strength and durability. They display more impressive speed, skill and agility though. Assuming the turtles' weapons can hurt the Asgardians, they take it.

Second fight is a bit closer. Despite his limited showings, Heimdall has been pretty badass. I think it depends on who draws first blood. If Shredder and Splinter can drop Loki quickly (Loki with the OP limitations is the weak link here), they can double team Heimdall quite handily. But if Heimdall scores a solid hit with that giant sword of his, whoever gets struck is going to be turned into a non-factor for the rest of the match. Going to go with team Asgard in the 2nd one. I think Heimdall could seriously hurt either Splinter or Shredder before either of them can put down Loki.

Hiemdall took down a space ship, a pretty large space ship

The Asgardians weapon and armor are no joke. Sif can casually kick a mobile home 30 feet and take shotgun blast point blank. I think the asgardians weapons win this fight for them. I don't think they will have a problem injuring the turtles while I don't think the reverse is true.

Her armor took a shotgun blast. The turtles were actually shown to be bulletproof and fast enough to block bullets with their weapons and dodge them. Also said Turtles did superhuman stuff like toss fully loaded cargo containers(weighing more than a small trailer on wheels) and hold up giant towers and stuff like that.

The Turtles are too fast, have weapons strong enough to hurt Asgardians and the strength to hurt them. They win that fight.

Heimdall while badass isn't all that fast from what we've seen, and as durable as the turtles were, Shredder hurt them just fine. And Splint had Shredder on his ass. I think they could fight Loki and Heimdall one on one until Loki gets taken down. Then if Heimdall is still up, they can double team him.