Rainwater in Heating Ducts

A little difficult to picture what you're describing, but a sump pump should be able to get rid of the water in the pits. As far as the water in the ducts, I don't know of anything but to seal them.

http://www.hometips.com/diy-how-to/sump-pump-install-replace.html

Are the ducts encased in concrete below the grade slab?

Water, water, everywhere, but not a drop to drink..Installed a heating cooling system in a Church in Ok. that was a down flow and did everything according to' hoyle'. Did put the pit below the duct so if moisture became a problem it would migrate to the furnace and could be disposed of..Attended the services a few months later and smelled water vapor,'a lot'...The furnace well was full after a large rain the roof water was seeping under the foundation. Used guttering and solved the biggest problem..The problem was the water???

Assuming that the pits are easily accessible- use a concrete saw to cut a 12 inch square hole- excavate it about 12 inches and install a stainless box with flanges secured to concrete with silicone, then install small sump pump and a water sensor to trigger pump at about 6 inches of water in sump.

For the duct work- your best issue is to keep the blowers running any time to keep ducts pressurized a little and to evaporate any water that seeps into the ducts.

Had same issue at a church that I had to deal with because installer did not think (like yours) about underground water so provided no seals on duct joints or any type of drainage piping.

You can also install some exterior drainage piping- perforated plastic with fiberglass screen covers to keep out most dirt- along exterior walls, below depth of the ducts, and connect it to a sump pump.