I will do some research..
The foul smell is a good clue. Oaks in FL get alcoholic flux, which is different from slime flux. It does NOT eventually kill the tree in many cases and it IS treatable by drying the infection out so it can be compartmentalized.
the goop on the sophora looks like a systemic bacterial infection that may have a chemical cure. Phosphite or bacastat or even paclobutrazol may be worth a try.
View attachment Ooze in the News small.pdf
even the utah extension folks in skwerl's link describe treatment, but this does NOT apply to Marcello's tree where the ooze is coming out of living bark. the below excerpt seems reasonable except for the oval shaping of the excision; that is misinformation. Because sap does flow laterally, it makes no sense to remove any healthy tissue.
If the fluxing is noted soon enough, the tree can be saved. Waiting and hoping the problem will correct itself often results in a dead tree.
Trees suffering from bark/cambial infections may be saved by promptly cutting away diseased tissue. On small branches it is best to prune the infected branch off at a lateral. With larger branches or trunk infections, remove all discolored bark down to the wood. Cut around the infected trunk or branch until you come to healthy, yellow-green cambium. In some cases this means removing a lot of bark...
The next step consists of shaping the wound to allow it to heal properly. Remove infected bark creating an oval shape. The long part of the oval should be parallel with the trunk or limb. Make the margins of the cut smooth and clean. Sterilize the knife with rubbing alcohol between cuts to prevent spread of the bacteria.
The final step involved cleaning the wound with a disinfectant such as rubbing alcohol or a 10% solution of bleach (1 part household bleach and 9 parts water). Watch the treated area for evidence of recurring disease activity. If tissue on the edge of the wound begins to flux, a spot of diseased tissue may have been missed.