IMO there are two tactics to take here. In H2H you're looking to win the most categories. Breaking it down:
Wins: Look for reliable pitchers on good teams, Middle relievers on great teams, or closers on poor teams.
Saves: Look for closers only
Ks: Starters will get 2-3 times the number of Ks that any reliever will get. An average starter will get about as many Ks as an elite level closer/RP will get. (take for example Eric Gagne who got 137Ks last year vs. an average John Thompson who got 136 Ks last year).
ERA: On a WEEKLY basis, you're looking for one of two things: Either conistency or mitigation. Consistency is what you'll get from the elite pitchers. You will get this from people like Prior, Keith Foulke, Pedro Martinez and so on. Mitigation comes from the average pitchers that can pile up innings. Starters like Carl Pavano won't get you 1.00 ERA performances often, but they also won't get blown up for a 27.00 ERA (which CAN happen to a closer from time to time). While you want the consistent great pitchers, you also need a few mitigators to put in for when your closers get beat up.
WHIP - much the same as ERA. You need both the consistent pitchers and the mitigators.
Putting it together, how do you win a minimum of 3 of 5 categories? Overall, closers will give you a better number of ERA, WHIP and Saves (giving you 3 categories). BUT - these guys don't pitch every day. If a team goes into a losing streak, you may go a week without an appearence. Or they'll get an appearence with no chance for a save. If that's the case, you've basically got a pitcher throwing 2-3 innings a week and that won't do much for your stats. Even with 5 closers on your roster, you may still end up with anywhere between 3-15 saves. I think getting more than 8 saves a week should be enough to give you a "win" in that category, so going for more just isn't worth it. To get that many consistently, you WOULD need about 5 closers, but 3-4 should be enough.
One strategy that has worked very well for me in the past is having 3 stud starters (the year I did very well I had Randy Johnson, Kerry Wood and Rick Ankiel) and 3 closers with 2 solid middle relievers. The three starters may or may not give me wins, but with 7-15 strikeouts a game, I would be getting (on average) 50-60 strikeouts from them alone, along with a great whip & era. The closers I had were not studs, but all ended up with 60 or so Ks in the year, and had 20 saves. That's good enough for an average of about 10 a week, giving me close to 70 Ks a week. That was often enough to win the category. The WHIP and ERA were also good enough to win usually, so I would win a MINIMUM of 2 per week, usually 3 and sometime 4-5.
That said, there are some problems with this strategy. First, getting three starters that will strike out 200-300 batters in a season is VERY difficult. Those are usually top 2-3 picks, and doing that will leave your batting & closing weak. What you'd need to do is find some sleepers. Maybe a Mark Prior #1, and then someone like Brett Myers ready to advance to the elite... or going after people like Johan Santana, Rich Harden, Josh Beckett who are not obvious #1s but could be had in the 3rd to 6th round. However, getting a top pitcher like Randy, Prior, Wood or Martinez is critical to this plan. If you can't get one of them, go to another plan. You NEED pitchers who are going to strike out 250 batters a year. And you need 2-3 of them. Fill out your pitching staff with 2-3 consistent pitchers (like a Woody Williams, Tony Armas, or Mark Redman) and use them IF you need to. Usually they can stay on the bench. You'd use them if you are short on starts in the week, if one of your normal starters gets beaten up, or if a closer has a really bad game.
This all said, going with "all closers" would not work well in head to head. It might in a normal type of rotissery system, but the week-by-week variances will kill an "all-closers" team. For example, if a pitcher has a bad game, he can end up with 3 runs in .2 IP. If you get those 5 guys to put in 10 innings in the week, and each of them has an ERA of only (for example) 1.80, the bad performance would raise that to a 4.22 which will probably lose you the category. And believe me, with very few exceptions, those 3-run games for relievers come around from time to time.