1" x 4"s will definitely be strong enough to support your weight. Used on edge, like joists, spaced at 24" on center, will be sufficient. Once the plywood top is fastened it acts like bridging between joists and will strengthen the entire assembly. I would not try to span more than 4'-0", with the 1 x 4s however.
I would use the 1 x 4s as is, i.e.. full size to make any L girders. Ripping them into 1 3/4" rips will compromise their strength.
Also make the legs using 1 x 4s in an L girder configuration.
If your layout will be free standing, not attached to any walls, you will need some diagonal bracing.
As for the table top, look into 1/2" OSB. There's no need to use birch plywood.
