Push-up : Şınav
Pull-up : Barfiks
Pull-up bar : Barfiks demiri
Crunches : Mekik or Sıkıştırma mekiği
Jumping jack : There is no literal translation for that, at least as far as I know, but you could say "Kol ve bacakları açarak sıçramak"
And to use them in a sentence, you might need to use the verb "çekmek", for example "şınav çekmek" for "to do push-ups".
push-ups: şınav , verb form: şınav çekmek
pul-ups: barfiks , v: barfiks çekmek
pull-up bar: barfiks barı
crunches: mekik , v: mekik çekmek
jumping jacks: It's also used in turkish.Never heard of a translation.You can turkishize it as "jumping jack hareketi".
a few more
chest pull: göğüs yayı
hand grip: el yayı
treadmill: koşu bandı
jump rope: atlama ipi