Hiiiiiiiii!
Yep, SAK was recently re-recognized by the school. I heard it had been operating underground for some time. A friend of mine is in the new pledge class. They're still really really nice guys! Never heard of the other, though.
Tri Phi-In the 80s, Loyola wanted all the sororities and fraternities to become national. Tri Phi became Delta Gamma. However, a small group of Tri Phis wanted to keep being that, so they are not recognized by the school and are forbidden to wear any jerseys on campus. I don't know much about it.
Currently, there are no local sororites on Loyola's or Tulane's campus. Not sure about UNO, Dillard, and Xavier.
BEGGARS is the oldest fraternity on Loyola's campus, and it was named so because the Pope had decreed no fraternities on campus, so a group of men went to the Pope and "begged" to have one. The Pope lifted the ban, and BEGGARS became reality.
Here's what we have:
http://www.loyno.edu/students/greek