Is that a dogwood tree? Sorry, the images are just of the trunks and it looks more like a pine! I see lots of damage that is due to woodpeckers (sapsuckers). They make these regular holes around the trunk of many different types of trees. In most all cases, the damage is superficial and does not become infected, however, the ooze you see means it has become infected. Injuries to trees can be colonized by many different organisms. When they get into the heart wood they can cause an anaerobic decay. This is the stink you smell. Gas is also produced and why fluid oozes out of the damaged area. The term we use is slime flux or bacterial wet wood. Here is some information on the sapsuckers:
https://pnwhandbooks.org/plantdisease/pathogen-articles/nonpathogenic-phenomena/recognizing-sapsucker-damage-your-trees

and then for the bacterial wet wood:
https://pnwhandbooks.org/plantdisease/host-disease/elm-ulmus-spp-bacterial-wetwood