Re: strength twice a week
Any of the compounds really if you're looking for overall strength:
DLs, squats, Oly, bench, press, dips, pullups, rows. Any work on rings..
Pretty much these and really any variation of those.
Obviously, good idea to keep the volume fairly low and the weights heavy.. 2x5 or 3x3/4x3 or something would probably work well with 2-4 lifts per session depending on how much you have in you.