Hola Emma

Yes, they are all synonyms meaning "to turn" in this context. I'd say they are all interchangeable although "doblar" is a bit more colloquial. So you can say:

Tuerce a la derecha / a la izquierda

Gira a la derecha / a la izquierda

Dobla a la derecha / a la izquierda

Also note that when using "girar" you are more likely to be in a car, instead of on foot. 

Saludos