You mention 'exhaust port', so that is one of the places you get oil, presumeably?
It's likely your pipe/cylinder joint isn't in too good a shape. With a minor tag (ding, hit, crunch) on the pipe that joint can get out of joint.
Remove the pipe. Clean up the mess. Put the pipe back on..hold it with just the springs (well, if you have springs) or with one, loose bracket. Start to put the silencer on and take note of what direction the pipe stinger has to move to match up with the silencer. Take the pipe back off. Place a piece of pipe or some other strong material in each end of the pipe and 'tweak' the stinger in the direction it needs to go.
Pipes are surpisingly pliable, especially an aftermarket pipe. OEM pipes will be a bit more challenging.
Tweak it a small bit at a time, then check the silencer fit.
When it does fit as good as you can get it to, put the pipe back into the cylinder finally with a good sized bead of hi-temp silicone. Bolt up the pipe hangers and the silencer. Let the silicone cure before you start the bike up.
Unless you have a mechanical failure of some sort (wallered out cylinder at the exhaust port or really bent up pipe that is out of round at that joint) that should take care of the goo coming out.
BUT...to get rid of the goo you will have to properly jet your bike.