Warning light cluster going nutz!

I'm sure this has been asked before but I'm too lazy to search all of the threads..........

I have some warning lights blinking on my daughters 1996 Intrepid. The "gas pump" light comes on and goes off continuously. I'll be driving along and the light will either blink or come on for several seconds, then go off. I know the car is full of gas cause I just filled it up! The "oil can" light comes on sometimes at an idle(not all the time) The oil was just changed and I know it is topped-off. Although i have not checked the oil pressure with a pressure gauge, I feel certain the pressure is good. Both of these items are in the same cluster on the bottom left of the speedo gauge area.

Since the gas light is freaking out, I truly think the oil light is doing the same. Anybody have any ideas? (besides shooting it of course!.....I have to much money in it to kill it now!)