I strained my quads yesterday after squatting. Should I stretch them out?

The intuitive answer for most people facing this question would be, yes. Perhaps, you figured
that you injured your quads in the first place because you haven't stretched them out enough in the past, so you should start stretching now. Bad idea. what?! but, why?

If you've strained your quads (or any muscle for that matter), then at the micro-level,
you've torn some of your muscle fibers; essentially, a strain is equated to damage to a muscle because it was either overloaded or overstretched during activity. Stretching the muscle right after an injury can actually worsen the strained muscle.

WWJD (What Would Jerry Do)? From a nutritional standpoint- Focus on getting the injured muscle healthier by drinking plenty of water, upping your protein intake (I would focus on whey and egg whites due to their high absorption rate into muscle), and
active rest. What's active rest? Avoiding activities that caused the injury in the first place.

Seeing a physical therapist can accelerate your recovery with a combination of modalities,
taping techniques to calm the muscle, and professional guidance. Stretching can be implemented after 10 days (past the acute stage of an injury) in a slow and gradual manner. After the acute stage, I recommend holding your stretches for at least 1 minute and perform the stretch for 3-5 times, several times a day because lengthening is best achieved with longer duration stretches performed throughout the day. There should be no pain when you stretch.
At the same time, if you're doing a pre-game warm-up, then shorter duration (10-30 seconds) is the way to go, because you don't want your muscles to lose their game-ready tone!