Robaxin is a muscle relaxant so your dog needs it. Put it down his throat if he won't take it buried in a bit of peanut butter or lunch meat. It's better to give with food to help minimize vomiting but at this point, it's much more important to treat his pain.
A dog in pain will not feel like eating. If you've ever really thrown your back out, you know how awful it feels. That's how he's probably feeling.
Give him the Robaxin and offer him some yummy treats -- even something off your Easter table such as LEAN, without extra fat, meats....offer him warmed-up chicken broth or chicken soup (it has important electrolytes in it). Gerber's baby food is also popular with dogs that don't wan to eat anything else.
You didn't mention your dog's breed or size....but in general, dogs can go 24-48 hours without eating; large dogs can go a bit longer without food compared to small breeds. The length of time without water depends on the climate where you live but most dogs should not go without water for more than 24 hours. Dehydration can make a dog that is physically hurting feel even worse.
You can further help your dog by carrying him up and down stairs and making sure he don't jump or further stress his back. In case it's his neck that is bothering him, raise up his food and water bowels so he doesn't have to bend over to reach them. Make sure he has a soft, padded place to lay down.
If your dog's pain increases and he still isn't eating by tomorrow, I'd have him checked out further. Other conditions, such as kidney pain, can look like spinal pain. You didn't mention if your vet ran any blood tests, but if not, then it would be wise to run blood and urine tests to check a variey of other potential causes for his symptoms.
I hope this has helped. Let me know if you have further questions.