When I fill my gas tank on my 2000 Dodge intrepid, the fuel gauge will move from full, drop to empty and then back to full again. It does this over and over until the tank is down to about 3/4 full.

The fuel tank has the Rheostat that has a float and on which the float moves up to change the resistance to the gauge which is a volt meter.
So you need to locate the fuel tank to see the fittings here, removal of the wires to the rheostat will change the fuel readings, so as to confirm the gauge.
If so remove rheostat and move float on the outside with the connection of ground and lead externally to confirm as you will notice the change on the meter.

well if you have it an empty fuel light came on to your dash, then you have travelled and just consumed the whole entire reserved gas in your tank, so when you are filling it up again, it will fill-up first the reservoir for your reserved gas then if it reach the minimum level of gas in your tank, then the fuel sensor unit will tell you now the exact amount of gas level on your gauge just keep filling it up (gas), DO not Press the entire trigger of the pump, just press it half way and moderate while filling -up gas so wont stop clicking and you thought that you have your tank full already but it was not.

sounds like a fuel level sender problem

sounds like you have a restriction in the fuel inlet pipe,( maybe air locking) also your tank sender unit neads replacing to fix you gauge fault, or it maybe that it has something that is not alowingf it to move freely inside the tank, have a good look inside when low on fuel. through the hole where the sender is fitted.

That's got nothing to do w the O2 sensor. The float on the gas tank is a good start w the gauge issue .

The sender unit in the tank is the most likely cause. To test the panel unit, remove the wire from the fuel tank unit and gound it. The panel gauge needle should move up full scale to hot. Remove the wire from the ground and the gauge should return to empty. If this test is ok, the tank unit needs to be replaced.

It sounds like the fuel sender is bad in the fuel tank.

Hi the gas gauge is erractic
you need to replace the fuel level sensor

the fuel level sensor inside your gas tank might be defective
you need to drop the tank and check the level sensor

open circuit in the fuel level sensor. mounted in tank. as the fuel level in the tank starts to drop the arm will move past the dead spot on the sensor and the gauge will start reading again.i dont recommend diy replacement of the fuel level sender.