9.16 The word here for "obligation" is anagkeh. It can also mean distress (The translators of Job use this word all the time in the LXX); even force or complusion! A reminder to all of us that preaching is both an obligation but also a source of stress. I wonder if this is true for those of us that love preaching just as much as those of us who like it less...
9.17 This is one of those grammatically ambiguous Greek sentences. Which "if" is hypothetical? Is Paul earning a wage or not?? It is not clear. One thing the translators hide is the word "oikonomia," often translated "stewardship." So Paul here is saying that if he does this against his will, than he has been entrusted with stewardship. This is an interesting thought on stewardship, where it would derive out of lack of will rather than our will!
9.21 The phrase "under the law of Christ" is rather interesting in Greek in that it is one word -- "ennomos" literally "in the law." It is an adjective in Greek, so it could just as easily be translated here "but I am legally Christ's!). In short, Paul does not make some distinction here between the law of God and the law of Christ. He just points out that he is legally bound to Christ.
9.23 The NRSV and NIV translate the word "synkoinoonos" as one who shares in the blessings. The NET does a more literal translation here as partaker. The point is that yes Paul is partaking, but I think the NRSV and NIV are fair in their efforts to capture the sense that sharing the Gospel does come with benefits. (Ie, the sharing implied by koinonia is real and not just touchy-feely). In this case though, Paul does not seem interested in his own blessing, but rather being a blessing to others.