I did a little math and, if Strasburg pitches every 5th day after 3/9, then he is lined up to pitch the exhibition against the Red Sox, open the season for the P-Nats on 4/8, and pitch in Bowie for Harrisburg on 4/13. 4/18 is a choice: Spot start the first time the 5th starter is needed at home vs. Milwaukee, or pitch a home game for Harrisburg v. New Britain. The thing is, he is set up for 4/3 and for 4/18 if he blows everyone away this spring.
It looks like Syracuse has a lot of home games in May. I could see him either sticking with Harrisburg maybe for another start or two after 4/18 (road, I think) and then moving onto Syracuse, or perhaps some more shuffling between the Nats, P-Nats, and Harrisburg to avoid cold weather until May.