Odds are your laundry outlet is Hot A, Hot B, and a Ground/Neutral - you'd have to verify if the neutral and ground are bonded in your panel, and try to figure out what side your dryer plug terminates to. More often than not, the dryer is running it as a neutral to help power some sort of 120v display on the control panel.
You can run a 240v setup all day long off this, but I wouldn't recommend trying to run a 240v/120v combined panel, as then you'd be using the ground/neutral conducto as both a ground AND a neutral. If you want to run both voltages, you'll have to run a dedicated ground to be safe. I'd also verify that it was actually a 50a supply and breaker, seems high for a dryer.
Like I said, you won't be able to safely derive 120v off this current setup, which is what people with a 4 wire setup do - Hot A / Hot B / Neutral / Ground - the neutral allows them to get 120v when combined with one of the hot legs.
Note - You will need to figure out a way to add a GFCI breaker or outlet or isolator of some sort in this setup to provide you a level of safety. Another reason to have the dedicated ground. There are some drawings on this board somewhere that P-J provided that show how to basically use a GFCI spa panel to go form 3 wire to 4 wire.
-Kevin