Two problems that I see:
1) Your present "three prong plug" is likely a 240V with ground. You need a 120V/240V with ground.
2) You will be over-breakered for the new unit even if you could use the old cable. No, you can't use a 50A breaker on a device that is limited to 30A of current.

Suggestion: Rewire for the new wall oven using 10/3 cable. The ground is included but not counted in the 10/3 designation. Replace the 50A breaker with a DP 30A breaker.

Thanks. I thought that was the direction I needed to go.

Wait a sec. Is the existing circuit cable, or is it in conduit? If it's in rigid conduit, I don't see why you can't pull a #8 green for the ground and use the other existing conductors. You'll have to change the outlet, of course. However, if it's cable, then yes, you'll need to pull a new cable.

With fixed and stationary appliances, the manufacturer provides a maximum permissible breaker rating for the circuit that the appliance is connected to. The UL/CSA/whatever listing depends on the curciut not being breakered higher than that. If it is, the warranty and the listing for the appliacne are void. So if the max breaker rating for the wall oven is 30A, you cannot leave the 50A breaker on the circuit, even though the circuit conductor gauge is large enough for that rating.

There is no rule against under-breakering a circuit. It's perfectly legit to breaker a #8 circuit at 30A.