Benefit (20): Paul wishes to benefit and be refreshed by Philemon, but not for his own personal gain. He was speaking of the debt that his beloved Onesimus owed, which he fully assumed (1:18-19). He sought the good of someone else at his own personal expense![1] Should Philemon void this debt, Paul would be delighted—not to mention Onesimus! Love sees others' blessing as its own.
Obedience (21): Although Paul hasn't ordered Philemon what to do, what is at stake isn't entirely voluntary. He calls it "obedience" because forgiveness was a demand of the One who forgives us (Matt. 6:14-15; 18:34-35). Paul hinted at this obligation when he called it "what is proper" in 1:8, and he even invoked the accountability of others (1:2). This said, obedience for the child of God is not burdensome. Hence, Paul is certain he will not only obey the Lord, but that he'll go beyond what is required.[2] Believers willingly please the Lord.
Visit and Greetings (22-25): Paul hopes that through their[3] prayers he'll be freed and will visit them. He firmly believes that God hears His people (1 John 5:14-15). With this hope, Paul asks Philemon to prepare a lodging for him.[4] Then, Paul ends his letter with greetings sent from those with him.[5] He wishes them[6] grace also. He always communicates this warmth in all his letters.[7]
[1] This is much like our Lord who went to the cross in obedience to the Father (Phil. 2:5-8).
[2] Paul leaves "more than what I say" undefined. Perhaps this is Christian ministry, greater care, freedom, etc.
[3] "Your prayers" and "I will be given to you" employ the plural "you." It points to all those named in 1:2.
[4] Given Paul's plans for Spain (Rom. 15:24), this visit will be in the future as with Philippi (Phil. 1:24-26).
[5] Epaphras is "a fellow prisoner [sun-aich-ma-lō-tos (συναιχμάλωτος)]" like Aristarchus (Col. 4:10). This does not necessarily mean in Rome at this time (cf. Rom. 16:7). The "you" (1:23) is singular, directed to Philemon.
[6] "Your spirit" has the plural "you." Paul expresses his final blessing to all the recipients.
[7] Every one of his 13 letters ends with a form of this wish. Cf. Rom. 16:20; 1 Cor. 16:23-24; 2 Cor. 13:14, etc.