Custom board cutoffs pcb
Yes, OSH Park will do custom board outlines. Just use the Dimension layer to draw the outline that you would like. OSH Park will attempt to fulfill your request as long as it is a reasonable(*) geometry.

For example, here's a board I had fabricated recently by OSH Park. I needed rounded cutouts in two of the corners:


(*)The definition of "reasonable" here can only be defined by the OSH Park people themselves. You'll have to ask them directly if you think your geometry is tricky.