First, I'd suggest that you focus on washing the scalp, not the hair, especially when you have to conserve water. Washing the hair just tends to strip it anyway and most people don't need to actually suds and wash the hair more than once or twice a week. (The exception being if you're working out regularly and using lots of product, but neither of those are applicable in an emergency situation). When you rinse the scalp the rest of your hair will get wet. You can use that to do a quick scrub of the hair without using extra water.
(edit: Also, combing the water through the hair at that point will help distribute it, eliminating the need to dump more water on the hair wet or scrub it. Use a wide-tooth comb to avoid hair breakage since it's often more susceptible to damage when it's wet.)

When you need to clean the scalp with no water witch hazel is often recommended. If you need something stronger you could try diluting tea tree oil. You apply either with a cotton ball.

When you have to clean the hair itself and have little to no water try a white vinegar rinse on the hair to remove dirt and oil. I've also read lemon juice can work. You can google for specific directions. It'll likely strip hair dye, but I don't really think that's a concern in an emergency scenario.

Another that helps to reduce the amount of water needed for hair washing is to comb out all the knots first, then use a spray bottle and a comb or brush to wet the hair. That saves tons of cups or gallons being dumped on the head. I've never done it but you could try using a spray bottle for white vinegar as well.

If you have long hair try to keep it up and/or covered with a hat or scarf during SHTF situations, as it will help keep the hair itself cleaner longer.