I don't know if you're crazy or not but you have company since I'm planning to do something similar. So I've also researched this problem.
I'm not an engineer so this is pretty much guess work.
If the following rough
calculations are right then it would take almost four hours for your heating element to heat up a 4 gal tank.
1 BTU is the energy needed to raise 1lb of water one degree.
1 gal/water ~= 8.3 lbs.
4 gal tank ~= 33.2 lbs
IF the water in the tank is 60 degrees and you want 120 degree hot water then you need to raise it 60 degrees.
60 degrees x 33.2 lbs = 1992 BTUs
1 watt = 3.41 BTU/hr
1992 / 3.41 = 586 watt-hr
If the heating unit puts out 150 watts then
586 watt-hr / 150 watts = 3.9 hours
I'm sure the real calculations are more complex than that. Any engineers in the crowd please jump in at this point.
Another consideration is heating an enclosed container. If you didn't see the whole Mythbusters episode check out this
Because of the danger I concluded that a DIY pressurized hot water tank would not be the way to go.
I'm look at a system that uses a espar coolant heater to heat the water. It seems the most energy efficient without having to go to propane. Since the hot water tank isn't pressurized there will have to be a after-tank hot water pump. That's the bare outlines. Haven't started building it yet so don't know if it will work.