Solid rods like you describe can be made to vibrate, but they are most resonant with compressive vibrations - hold the rod loosely at about a fourth of its length, and strike it on the end - it'll ring like a bell. Glue a thin disc of steel on the other end, and put that over a magnetic pickup. Only problem is, to get 4 notes, you'll need 4 different length rods. For bass notes, you'll need really long rods.
If you try to use rods like that with the movement being sideways (like a stringed instrument), you'll learn really fast why strings are wound, not solid. Solid rods have a lot of inherent stiffness - in flex, they're a dispersive medium, and the velocity of propagation is not constant with frequency. Practically speaking, that means the overtones of the vibration are not harmonics of the fundamental - the thing will sound out of tune with itself.