Small Engines (Lawn Mowers, etc.): John Deere STX38 Engine Vibration

Question
Hello.  Just recently my John Deere STX38 (black deck)with a 12.5 Kohler engine started vibrating and making hard knocking sounds right as it turns off.    Appears to run okay, maybe a little rough.    I changed the air and oil filters, the gas hose line, changed the oil and the spark plug.   After noticing a gas  puddle below the brand "new" JD air filter and a trace of oil residue around the bottom of the filter frame, I cleaned out the carb with gummout (not my first choice) yesterday.   I am wondering if I should get another air filter?   After all this, the vibrations and hard knock (clunking), right before the engine is about the stop, is still there.  It now also blows out a puff of black smoke when it starts up.    During my last lawn cut the edge of the mowing deck clipped a tree hard enough to knock one side (of the deck) off its back support.    I am wondering if this could have bent the cam shaft... but it is  belt driven.    Could it have upset (unseated) a value or push rod, or damaged the driver belt?  The engine does vibrate a little when running (without cutting deck engaged).    I also checked the oil and it does have a faint smell of gas.   It does have a fuel cut-off switch that I never thought to use (cut-off when not using) in the past... I do now.   Last but not least, it appears that there is a trace of oil leaking from the bottom of the engine (between bottom and mower frame) but this could be residue from an older oil change, as it is a trace.   Well, I believe I covered everything and I'm ready to try anything to solve the issue... if it can be solved.   I bought new drive and deck belts last year, but only installed the deck belt.  I am wondering if I should go ahead and change the drive belt.   Any thoughts would be appreciated. Thank you, Novice at heart!

Answer
Does the mower vibrate when the blades are not turning?

Have you checked the engine mounting bolts and crankshaft pulley to see if they are tight.

It is not likely you damaged the engine camshaft or any other internal engine parts.  A bent crankshaft can cause vibration but again very unlikely the crankshaft is bent as the belt will stretch before damaging the shaft.

Is the vibration you feel from a rough running engine?  Has the carburetor ever been removed, dis-assembled and cleaned with compressed air from an air compressor?

Eric