Can I have an electric dryer, a washer, furnace, and gas water heater all in one laundry room?
Only issue I can see is where the makeup air comes from. The washer doesn't matter, but if the dryer, furnace, and water heater all turn on at the same time, they each need air input. Putting everything in one room can cause an issue where it's easier to suck air through the output of another appliance than suck air from inside the house, and that can leave carbon monoxide inside the house. 

The input air can come from inside the house (in which case there should be some sort of vent in the door or something), or outside (in which case you should be able to see the vent.)

I would also highly suggest installing a carbon monoxide alarm somewhere in the home if not already present, and testing it if it exists already. This is general advice whenever gas appliances are in use.