Certified GKH Gardening Expert
Are they bitter, or sour? If bitter, I'm not sure what is going on, possible nutritional deficiency and/or inadequate water or too much shade to facilitate photosynthesis of sugars.
Juice oranges in Arizona, like Valencia, are usually grafted trees. Sour orange (Seville) root stock is used because it is hardy and resistant to soil borne pathogens. The desirable orange variety is grafted on to the root stock and suckers originating from below the graft should be removed.
If the fruit is extremely sour, I suspect that what has happened is that a sucker or multiple suckers have grown up from below the graft, from the sour orange root stock and dominated a portion of the foliar crown. The only way to rectify this is to remove the stems that originate lower on the tree trunk, from below the graft. If the tree has matured with this anomaly, it may be best to do this in stages over a period of two or three years, so as not to remove more than 25% of the foliage in a one year period.
An alternative is to make marmalade from the sour oranges.