The textbook answer for fertilizer is to have your soil tested and find out what's missing. The state of NC does it free for landowners, perhaps Indiana does the same. Best to contact your county extension agent, who would also be an excellent resource to see your tree in person and make recommendations. Without soil testing, a basic 10-10-10 applied according to the directions on the package would be a good starting point. It's better to under fertilize than over fertilize.
Pruning would not cause the symptoms you're describing. Typically, a tree's reaction to improper pruning is to grow more branches and leaves.
Leaking sap can be caused by a couple of things. Woodpeckers going after insects can punch a lot of holes, although the insects are generally in areas of decay in the tree--areas less likely to leak sap. Check the tree for small holes that might be caused by insects or birds boring through the outer bark.
Another possibility is a bacterial infection, which is more likely than birds and bugs, although bacteria still need a way into the tree. Sometimes bacterial infections smell, so give your neighbors something to talk about and sniff your tree (really!).
Lastly, mulch is a wonderful thing. It moderates soil temperature, retains moisture, aerates the soil, makes it easier for water to move into the soil, and keeps the nasty yard tools away from the trunk.
If you're really committed to saving a dying tree, you might try contacting a certified arborist. The good ones have the tools and knowledge to treat things like infections that would have us foresters and sawyers saying "Time to make some lumber." Good luck.
