1 Cor 9.24 Corinth was home to a famous set of games (not quite as big as the Olympic games, but quite significant); Paul writes using very familiar imagery when he refers to athletic competitions.
9.25 The word here for "strive" or "fight" is "agonizo-mai" (in English -- agony!) This is used in 1 Tim 6:12 "Fight the good fight."
9.25 The word here for self-control is the verb "eg-krato-mai." krato is from last week (control; govern; power); eg from ego; the mai is just a deponent/reflexive ending. Thus, you might even say that Paul is advocating self-governance here ;-) He also uses this verb in encouraging people who cannot control themselves to marry in chapter 7. The noun form of this verb occurs a few times in the Bible, including Acts 24, when Paul is talking to Felix; Galatians when Paul discusses Christian fruits of the Spirit (5:23) and 2nd Peter, in terms of how we should grow in Christian maturity.
9.25 The word for perishable, "phthartos" (trying saying that one outloud), is also the key word of 1 Cor 15 -- the perishable will put on the inperishable.
9.27 The word here for "beat" is "hypopiaz-oo" which refers to the part of the body underneath the eyes that gets black and blue. In short, the Greek here does not soften what Paul means! This word is also though used in Luke 18:5 in reference to the unjust judge and the widow who "wears" him out.