Welcome. I'll let the proper DC residents comment on the real ins and outs of parking. The laws on the books suck a bit, and are even countermanded in some cases. According to DC, motos are supposed to park parallel to the curb except in moto specific spots that are painted for perpendicular parking - oh DC.
Parking on the sidewalk is tempting ticket fate a bit. Motocycles are not allowed to park on sidewalks. And DC definfes anything but mopeds as motorcycles. Yes, even a 50cc Metro scooter is a motorcycle in the district. Supposedly this is under review, as the code is written pretty goofly and note in tune with VA and MD.
http://www.dc.gov/DC/DDOT/On+Your+Street/Bicycles+and+Pedestrians/Bicycles/Non-Traditional+Motor+Vehicles+and+DC+Law