I am having leaks into my utility closet (hotwater heater, ac&heating) which is between two bathrooms from upstairs. It sounds like water is running while in either in bathroom. How to determine where leak is coming from?

Start by shutting of your main water supply to the home. This will start to narrow down if this is a plumbing or heating issue. Let me know what you notice with the main closed.

There seems to also be water in the main vent duct coming from the heating/ac unit.

Have you closed the water main to see if that changes anything? Try that. Some heating systems produce condensate, does yours?

Thanks so much for helping... There was a small hole in the pipe running from the hotwater heater. It is fixed now! Again thanks...