Money is tight right now so I can't spend to much on the plot. So my question is: Is there anything I can plant with this pH level that will grow well without adding lime? The area recieves a good deal of rain.

Buck wheat will grow in low ph like you have. Plant after last chance of frost. Till or disc under around Labor Day and plant Rye [grain not grass]. Buckwheat is great for improving soil when you disc it into soil. It will not improve your PH, the only thing that will help that is lots of lime. Deer will eat buckwheat and also use it for cover for fawns. The rye will stay green thru the winter and give the deer a food source from the time that it sprouts until late spring of next year.