Lots of smoke and low power

This small engine needs a 40:1 ratio. Use only 2 cycle oil, not motor oil. If you are mixing one gallon of fuel use 3.2 ounces of the 2 cycle oil. This should give correct mixture so you do not get lots of smoke when you start. Take the time to measure. Note: there should be a marking somewhere on the engine about the mixture.

run fault codes and look for misfire and faulty injectors . Have a pressure test done on the fuel manifold as low pressure will result in your description.

Clean orreplabe carborator

first make sure your air filter is clean. and make sure your oil level is correct.
lack of enough air will cause a lot of smoke and poor fuel economy
lack of air would show as gray to black smoke.
oil burning would be light gray to white

sounds like the mix is to rich.dump out. mix gas again.check plug for fowling.replace plug if so and try starting again

IS THE CHECK ENGINE LIGHT ON.IF YES COULD BE FAULTY PCM.BUT HAVE CAR CODE SCAN TO MAKE SURE BECAUSE YOU COULD HAVE A FUEL SOAK CHARCOAL CANISTER , WEAK IGNITION SPARK, FAULTY FUEL PRESSURE REGULATOR.AND LOW CYLINDER COMPRESSION ALL OF THESE THINGS WILL CAUSE BLACK RICH SMOKE MIXTURE.

Hello,
My name is Dane and I am going to try to help you solve your problem. Are you sure nothing is rubbing outside the engine creating the smoke? If this smoke is indeed coming from the exhaust, I would think that your problem has to be in your fuel. You may have mixed too much oil in the mixture or it has been contaminated with water. Remove your spark plug and make sure it isn't oil fouled. If you find it is, drain your fuel and either clean with a wire brush or replace the plug. Refill with properly mixed fuel and you should be good to go. It may smoke for a couple of minutes until the fuel in the lines works through the carb though. No harm done.
I hope I've helped. If you found this information useful, please leave feedback as deserved. Thank you! Dane

Let it cool down, then add water to the radiator, not the recovery bottle. Re-start it and check for leaks. If while checking, it overheats, replace the thermostat and do it again. Replace any leaking items.
If you badly overheated it you may have damaged the engine. If it won't start or makes a lot of noise or, you see lots of white smoke from the exhaust then you have a large problem. (time for a shop)
If everything is OK, then remove the lower hose at the radiator and re-attach it, then refill the system with the appropriate amount of antifreeze (small inexpensive hydrometers are available at most parts houses. You want a 50/50 mix.) Always run the heater on high heat to avoid having air trapped in the system while re-filling.

Carb adjustment. There is usually a HIGH and LOW fuel mixture adjustment on the carb. Sounds like the LOW needs to be adjusted. Do a search on the Internet for a service manual for your particular model/make. Simple job IF you have the manual there for guidance.
Good Luck

Sounds like maybe one of your injectors is know working, I would start with that. Please let me know if this helps. Any other questions on this please ask.

Cheers