Quote (my emphasis):
"The only thing I want to know is if the highest allowable MTOW (ex: for the longest runway in the world with no obstacles ahead) for the MD-82 (149500lbs) permits it to continue and takeoff with just one engine."
At sea-level on a dry runway with zero gradient, certainly. Otherwise the whole concept of MTOW would in practice be meaningless? But, when considering the acceleration phase on the runway, there has to be an airspeed calculated below which it is not safe to continue in the event of an engine failure. The nominated V1 (decision) speed has to take that into account.