2 X 4' on 24" oc should be fine for walls and rafters for a small shed....rafters may be a concern if there is heavy snow load in winter...better to go with 16" oc and 2 X 6 rafters to be safe if there is a chance of heavy snow. Tie opposing walls together at the top plate as well with 2 X 4's every 4' apart to keep them from bowing out. Floors would be better with 16" oc joists to prevent bouncing effect/sagging with 3/4" plywood flooring...not chipboard... and 2 X 6 floor joists would be better if heavy objects will be in the shed....no need to go with 2 X 8, 10 or 12 for a simple shed. You could also support every other floor joist at midspan with cinder blocks or other solid blocks between ground and joists to help keep the floor firm and avoid using wider planks/joists.

24" oc the walls are fine.. It can be done for the rafters too but it will depend on the pitch you put on it. Especially if you have any amount of weight such as winter snow.. Floor joist is a big no no with 2x4 and 24" oc.

2x10 or 2x12 for joists 24" oc and with a 1" subfloor to prevent sag between the joists.. Better of going 16" oc on the floor to prevent sag between the joists.. Most important is to check local building codes to protect yourself.. GL

If your roof trusses are @ 16" centers, at least the walls that support them, the side walls, should be @ 16" centers.

I'm building a workshed that will be 12x16ft. 7/16 OSB sheathing. I was going to use 24" on the floor joists anyways. Do you should it would effect anything to any great extend by changing the wall stud span from 16" o.c. to 24" o.c., as well as the rafters? Not only will it save time and money, but less heat transfer through the studs. But I am not too experienced in this, so I'm worried it might cause structural failure. Most likely not, but I'd like to know what others think first.