Decks, Patios, Porches and Docks - Drafty overhang?

I need to seal up a drafty basement overhang-joists extend beyond foundation. The basement's ceiling joists extend approx. 2ft. beyond the foundation and the first floor kitchen sink is located directly above this overhang. The overhang is sealed by 2ft. sections of what I think is a vinyl soffit and a layer of fiberglass insulation covers the soffet. During the winter the kitchen pipes freeze and there is a noticeable draft at the base of the kitchen sink.
I am assuming that this condition was the result of shoddy construction. I was considering sealing this overhang by leaving the soffet in place and fixing 15inch strips of plywood and/or exterior Styrofoam sheathing between the joists.
Although I understand that water pipes are prone to freezing when they are near an exterior wall; I am wondering if this plan would work? What is the purpose of a soffit and is this really a soffet or just vinyl siding?
The temperatures are dropping so your input would be greatly appreciated.

http://i12.photobucket.com/albums/a247/dimc2828/IMG_0411.jpg
http://i12.photobucket.com/albums/a247/dimc2828/IMG_0403.jpg
http://i12.photobucket.com/albums/a247/dimc2828/IMG_0407.jpg

Thanks,
Dave

The purpose of a soffit is to prevent insects and animals from entering. It can be vinyl or wood.
If I understand correctly, the joists extend beyond the top of the basement foundation wall. Are these spaces closed in between the top of the foundation and the kitchen sub floor? If so, I would open them up to allow basement heat to circulate and apply insulating foam and insulation batts to reduce the transfer of cold air into these areas.

The overhang area is open to the basement. Are you saying that I should remove some of the insulation from the overhang area? And how would I attach the insulating foam to the joists? Will I be able to seal the area without using plywood?


http://i12.photobucket.com/albums/a247/dimc2828/IMG_0411.jpg
http://i12.photobucket.com/albums/a247/dimc2828/IMG_0403.jpg
http://i12.photobucket.com/albums/a247/dimc2828/IMG_0407.jpg

Start By Rmoving The Soffit Materials Carefully. This Should Show The Joists Then Add Batt Insulation To The Area An R - 30 Or So . Then I Would Us A Quarter Inch Ply Wood To Seal The Insulation Into The Space And Them Replace The Soffit Material.this Is A Pretty Common Thing That I Have Had To Deal With. Reusing The Soffit Just Gives It A Finished Look.