There's solid-state devices which can do what you want. I use the BTS716G a lot and I'm sure it's got bigger brothers with the current capacity you need. Or search Google for "high side switch with open load detection".
If you must keep relays, feed 5V to each relay output with two large resistors in series on each one. Like 10K or 1M. Then connect the mid point of those resistors to an Arduino input. When nothing's connected it will be at 5V and will read high. When you plug in the compressor, it will drag the voltage down. You may need to experiment with the resistors available to you to find a combination that works. (This can also be calculated using the Atmel datasheet which shows you the digital high and low levels.)