Bend it. If it snaps, it's styrene. If it doesn't snap, it's vinyl. Simples...
Alternatively, hold the record with thumb and index finger by the centre hole and rim, lightly flick the record with a finger nail and listen to the sound. Styrene sounds tinny, vinyl sounds dull. Play the record - if it starts with a short hiss, chances are it's styrene. Styrene is easily discoloured by solvent so be careful when cleaning records with lighter fluid in case you accidentally discover it's not vinyl. Err, that's all I can think of...