I just started playing Onigiri again after a year or so of not playing, and I was wondering what the letters are next to Youkai names in the field and also on the bestiary mean/what their effects are? (S, M, B, etc.) Thanks!

Those letters stand for type of youkai. B = Beast, M = Monster, S = Specter, and SL = Soul. This has been added to the game a few months ago and it only affects partners (exclude the normal ones). Generally, Beast > Monster > Specter > Beast ; Soul is like in the middle. Vanguard partners are also strong and weak against certain type(s) of youkai.