I have what I think of as a "standard US electric standby water heater." I will update this when I know the model; I am out of town right now.
It is located in a cold, cluttered closet in a cold apartment. Would the efficiency of the water heater be likely to increase if I took some of the junk out of that closet?
What other factors might affect the answer to this?
The heater already has insulation. The cluttered mess of the room it's is in will have exponentially tiny effect on the efficiency. Unless it was perfectly air sealed and insulated, but even then, most of your loss is in the pipes on the way to the tap.
The best thing you can do with your current system is insulate the pipes. You can buy foam insulation for this purpose at any hardware store. It will not help the first time you turn water on for the day, to be honest. But it's something.
Best case scenario is that you have the temperature setting too low and can turn it up to get hotter water.
Next best scenario is that it needs to be drained and cleaned, maybe even descaled (ask a plumber) and that will give it some new life.
For electric, if anything clutter will act as insulation, but realistically no effect.
Gas is an entirely different story, as you need to have air flow for combustion and the exhaust can be very hot.
