what would cause condensation in attic the osb is totally saturated?

Sounds like you have an "ice damn". You should be able to search the internet using that term to get some good diagrams. Looking at the attic floor; can you see the tops of the rafters/truss' that the below ceiling is attached to? That would be one indication you do not have enough insulation. If you have the fiberglass batts laid out there should be two layers. If you have a loose fill such as cellulose (gray) or ground fiberglass you should have at least 10". You want the attic insulation value at an R-30 or better, new construction in our area currently have R-42 (central WI). The insulation creates a blanket over your upper ceiling of the home, anytime the insulation thickness is lacking or you have specfic voids or gaps in the insulation this provides warmer air in the attic which in turn melts snow on the roof. When the melted snow gets to the roof edge it then can re-freeze creating "ice damn", this then backs up on the roof and can then weep/leak back into the attic.

Excesssive moisture in the attic is usually means one of three things:

There is not enough venitllation to remove the warm, moist air from the attic

The vapor retarding barrier is not properly installed

Their is not enough insulation and the attic is being warmed faster than it can vent.

From what you describe, I would say it is a combination of 2 and 3. Kraft faced insulation does not provide a sufficient vapor barrier. In my state (Minnesota) a 6 mil plastic barrier is required. This has to be caulked to the walls and taped to all electrical boxes. An air to air heat exchanger is also required to vent moisture from the heated part of the house.

It sounds like this is new construction. If so, and you are heating the space with "salamander" heaters, you are pumping gallons of water into the air. (Electric forced air or baseboard heaters are a better way to heat during construction.) This would explain the condensation in your attic.

The short term fix might be to install a powered roof vent to increase air flow in the attic. But when the weather warms and things dry out, you will need to address these other problems. A good layer of blow-in cellulose or fiberglass insulation and an air exchanger would probably solve the problem. If the air exchanger 12-15 hundred is not practical, the insulation alone will help a lot. Just be sure things are dry before you bury them. (Mold issues)

hope this helps.

leave your Attic door open, for a couple of months, needs ventilation

lack of ventilation

could be a leak