who mixes with who?

That is a time-consuming answer. If you're not really involved then don't worry about it.

I'm banking on somebody being bored enough to answer.

Big 4, SAE and Chi Phi - Tri Delt, KD, XO, ADPi
Chi Psi and Kappa Sig- same but to a lesser degree and ZTA, AXO and Phi Mu
Sign Chi, Sigma Nu, ATO and Pi Kapp - AXO, ZTA, Phi Mu, Alpha Phi (with Sig Nu cause they probably paid for it)
Pi Kapp and Pi Phi
I don't care about the rest

It kinda varies year to year, but for the most part:
DDD/KD/XO mix with big 4 mostly
ADPi mixes with big 4 sometimes, Chi Phi, SAE, and I think they've mixed with Sigma Chi before
ZTA has mixed with Sigma Nu and Sigma Chi and maybe Kappa Sig
AXO mixes with Sigma Chi, Kappa Sig, has mixed with Pi Kapp, and has also mixed with SAE a couple times
Phi Mu is always Chi Psi, ATO, Sigma Nu, repeat
Pi Phi mixed with Pika and Pi Lam last year and are mixing with Zete this year
Kappa has mixed with Lambda Chi and Sig Ep this year and KA last year
Sigma I'm not totally sure about. I know they mixed with Alpha Sig last year, not sure about anyone else