los

You need to have at least 1 rec for all of the sororities on our campus. That is the minimal amount. If possible, get more than 1. I would say 2 recs and 2 letters, or more.
Recs are more formal than LOS. They will have your resume and picture and things like that. LOS are more informal. They are written on something like the lady's stationary who is writing the LOS. They basically say how great you are and how they would love for you to be a part of their sorority. Recs are more important.
Once you have 2 recs for a house, if you find more women then I would get them to write LOS instead of recs, but that is my opinion. So if you can only get 2 people for one of the sororities, then get them to both write recs. If you can only get 1 person, get her to write a rec. If you can get 4, do 2 recs and 2 LOS. If you get 8 people, do 2 or 3 recs and 5 or 6 LOS. Etc.

If you do not have one rec for every sorority, you run a huge risk of being cut from the houses you don't have a rec for. Having just 1 rec for a house makes sure that you won't be cut for solely not having a rec. You could still get cuts for other reasons though. It would most likely help you to have more than 1, but as long as you have 1, you should be fine. If you can get more, than that is no doubt what you need to do. But if you have exhausted every source for finding ladies to write you something, then as long as you have 1 for each sorority you should be fine.

There is all kinds of useful information on the ole miss Greek life page. You should read it! There is a page that lists all the alumni Panhellenic associations. I suggest you locate the one closest to you and call them!

Dos.orgsync.com/org/umgreeks/nprecruitment.

Same page will also walk you through recommendation letters.