Alot of time, if there is too much oil in the motor, overfilled, this will happen. Also, if you tilt it for too long a time. Just check for the proper oil level and it will eventually stop smoking. No harm done.

"or would having it sitting at an angle like this cause the fluids to run out. "

Well partially.
Smells like gas? Did you stop to think why?
Because sitting at an angle, the carb float doesn't seal off the fuel flow to & through the carband gas just keeps running into the sump until it overflows and runs out somewhere else.

With your oil so diluted, engine life is extremely compromised.

Ensure to dump your oil and refill with fresh oil of correct Sae , as Bill has advised Oil contaminated with gas can easily wash out a bearing in short order . Also check your air filter for any contamination and either clean or replace.

thanks for the responses.

Thought that it was possible that the gas could run straight through, but was surprised by the volume and like I said wasn't sure if this was a sign of something else.

Both gas and oil can run out when you turn an engine over on the carb side. That's what happened to yours. The gas coming through the muffler picked up carbon and turned black. The oil might have been black already from being over-used.