Interesting combination of schools, and I happen to have worked at two of them! I spent four years at Temple, and then 19 years at LMU.
None of these is a bad school, so there is no obvious, "Don't go to that one!" answer because of quality. You will get good faculty at all three. Both St. John's and Temple are large schools, while LMU is small-medium-sized. There is a big difference between going to a school with 40,000 students and one with 8,000. At one, you will have a lot of options (many majors, many choices of courses), while in the other you would have smaller classes and more personal attention. At LMU you get to know many of the people around you, which isn't necessarily the case at places like Temple and St. John's.
While both LMU and St. John's are Catholic schools, neither is horribly stringent, and religion is available if you want it, but it isn't forced on you constantly. At Temple, it really isn't part of the equation.
LMU has a gorgeous campus, while Temple does not (unless you are at the Ambler campus, which is very nice, but not spectacular). I've never been on the St. John's campus. If sports are an issue for you, you get more at the larger schools, especially if you are into football (but none is a really good football school).
Diversity takes different forms at the three schools. Both Temple and, as I understand it, St. John's have fairly large African-American populations, with smaller groups of Asian and Hispanic students, while the diversity at LMU would be reversed, mirroring the local population. Economic diversity would be greater at Temple, which is one of the less expensive schools in the area. When I was there, I had a lot of first-generation college students in class. Temple used to have a slogan, "They could have gone anywhere, but they chose Temple." I had students there who had been accepted to places like MIT, but couldn't afford to go there. I also had students there who were functionally illiterate. While Temple's standards have increased, I understand from former colleagues that this is still somewhat true. There was a smaller range of ability at LMU. It was rare to get a truly outstanding student (I had more in 4 years at Temple than I did in 19 at LMU), but equally rare to get someone who was really inadequate. My understanding of St. John's is that it lies somewhere in between.
For me, because I can see advantages in both larger and smaller schools, and because I don't have any really clear geographic preferences, it would come down to my intended major, or at least the general area in which I expected to study.
