8 AWG can be used when the proper wire is used, all components are rated at 75 deg C or 90 deg C (breaker, wires, conduit, etc.) and you don't have to de-rate (either due to high temp attic runs or packed conduits, etc.) There is no easy guide for this because the NEC deals with different wire types. For example, if you used type NM cable (typical all-in-one black-sheathed Romex multi-wire cable, like 8/2) it isn't good for 50A with #8, but separate wires in conduit or type MC cable is ok. You have to check your wire / cable's ratings and types.
EDIT: Oh yes, and the length of the circuit. #8 for anything longer than a short garage run should probably be avoided.
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A few things:
1. Since you added a new outlet, it must conform to code. An electric dryer and a range/oven may not share the same circuit.
2. When you say they're on the same breaker but not the same wire, and you installed this breaker, did you attach multiple wires to each screw terminal on the breaker, or are they pigtailed together inside the box? They must be the latter - even if it were legal to share the breaker, you cannot have two wires connected to a breaker screw, to be legal.
3. What breaker was formerly in the box? Wiring, receptacles / appliance nameplates, and OCP devices (breakers) must be matched. If your oven was a 30A oven on #10 wire it cannot be connected to a 50A breaker.
4. Given your location, I am assuming that your county / city subscribes to current code and requires inspections. Installing a new breaker and outlet will typically require a permit and inspection. If you didn't do this, selling your house later may create a problem -- in some jurisdictions, it can cause you to have to bring the ENTIRE HOUSE up to code at your expense before you may sell it. You should check with your city hall / county inspector.
What type of panel do you have? Some panel brands have compact breakers, 2 in one slot. You could combine 4 120V circuits into 2 slots to make room for a new double-pole breaker. Before you do this, you'll probably need to do a load calculation to make sure you're not going to oversubscribe your panel too much, since you're adding such a large load.