Can you have strabismus without your vision being affected?

Strabismus. Yes. Some people with strabismus have double vision and reduced stereo vision (depth perception). Many people with strabismus see very well-- they do not have double vision and their eyes work together well. It is simply a matter of degree, since the brain can compensate for small amounts of strabismus. See you local eye doctor if you are having double vision or trouble focusing.
Yes. Longstanding strabismus is usually compensated for by the brain which uses only one eye at a time, suppressing double vision.