There are quite a few listings for this service in Austin, Texas but none offer a price list. I suppose it would depend on what you need to get fixed and if you have insurance.
Yes there are 24 hour emergency dentists in LA county area. The Santa Monica Emergency Dental Clinic is one place that offers 24 hour emergency dentist services.
24 hours dentists are somewhat profitable. They do not make much more than what the average work hour dentist would make, but the 24 hour option would get more customers who otherwise cannot schedule...
I am not able to tell you where to find a twenty-four hour dentist because I do not know where you are located. I suggest looking in the yellow pages of your phone book.