I have a bryant furnace, model no. 383kav036070 that, after the furnace comes on, and the blower squirrel cage turns, it makes a "clicking" sound, like the squirrel cage is touching something? Can you oil the above blower motor, and, should I call a technician?

Most motors today do not have oil holes since they say they a permanently lubricated and if you believe that one I will sell you a bridge to nowhere. LOL

The ones today have oil impregnated bushings that last a long time but not forever.

If this is the main blower for the furnace that blows air into the home it could have sucked something in that is causing the noise. Make sure to shut the power off then remove the blower access door and check. If you cannot do that then you might want to call for On Site service now or wait till the noise gets a bit worse.

It is also possible the motor shaft that the blower wheel on it has worn and is moving back and forth. You can check that by grabbing the shaft and trying to move it back and forth to see how loose it is. To do some of this testing you might have to remove the blower assembly from the furnace. Usually it is held in place by two 1/4 or 5/16 screws. Then you just slide it out after unhooking the electric. Good luck and I hope you find the noise.