I like to occasionally think of how everyone in the SDM would defend themselves if it was under siege by an army of oni, or by a legion of paladins seeking to cleanse evil, or by gas mask wearing soldiers with shotguns and assault rifles. But in this case, it's tyranids.
I'm not too familiar with them and the 40k universe as someone who actually calls themselves a fan of 40k would be, but I think Remilia and the SDM would do fine against them. Hong Meiling would be breaking them apart with her fists and feet, Patchouli would be eliminating large crowds of nids with her powerful magical spells, Flandre would be able to destroy any tyranid by crushing the "eye" of whatever part of their body enables them to do anything (like their brain or their heart) and Remilia would be tearing through the enemy hordes with her great spear. Everyone would be weakening/killing nids with danmaku. If worst comes to worst, Remilia would be able to summon hordes of devils to help defend the mansion.
As for me, I'd want to be piloting a turret or something if we had access to that. Flan and Remi would turn me into a vampire on the day we meet, so I'd probably be doing my part and tearing into the enemy hordes with blood magic or raw physical force if needed.