Thanks for the heads-up on the hose Speedy25. The inner surface of the hose looked more like that of french fries

than rubber. I cut the hose open and it would just crack all over as soon as I bent it. Installed new hose and it holds tight.
As for the pressure, I talked to a Toyota mechanic and he said that it is in fact reduced from what the pump supplies. The oil would flow too quickly through the cooler otherwise, since the return line goes directly to the oil pan.
Here are some pics after repair.

This is the connection that was leaking. Right where the yellow dot is on the black rubber hose.

The lines go under the condenser to the bumper on passenger side.

View from the front

The lines turn towards driver's side where the cooler is mounted.

The oil cooler. On the driver's side.