O.L. stands for overload, that is, a large resistance that's outside the range of the meter.
There are two things suspicious in post #15:
1. You measure "no resistance" from the solder joint between R3 and R4 and the ADJ pin. If no resistance means O.L., the connection from the feedback network to the LM317 is interrupted, which would cause the LM317 to make the output voltage as high as it can.
2. The weird low resistance between the LM317's input and output, which seems to indicate either a damaged LM317 or some short across it.
There are two things suspicious in post #15:
1. You measure "no resistance" from the solder joint between R3 and R4 and the ADJ pin. If no resistance means O.L., the connection from the feedback network to the LM317 is interrupted, which would cause the LM317 to make the output voltage as high as it can.
2. The weird low resistance between the LM317's input and output, which seems to indicate either a damaged LM317 or some short across it.
Be aware, those regulators require a small load of around 10mA in order to be stable at regulating.
Judging by the measured voltages of post #9, the feedback network is loading the regulator output, although it may not be connected to the ADJ pin. The colour codes of the resistors in the pictures match the schematic, and the ratio of the measured voltages across R4 and R3 in post #9 is about 11:1, as it should be, but both voltages are too high.