It's a 1984 chevy camaro with a 305 engine in it. I took the 02 sensors out. Will this effect anything? It doesn't have to pass emissions by the way.

The computer uses the O2 sensor reading to adjust the idle and cruise mixture. Without it you'll probably get an SES light and go rich.

Running rich, hesitation @ idle and light acceleration, some misfiring, will ruin your cat if equipped with one due to rich condition. Your car will basically run pretty inefficiently because it is not adjusting fuel trim as well as it should because it is missing a high priority sensor.