No brake light,no turn signals , no flasher lights...I have checked fuses for each and they are OK. Also all bulbs are OK. Any suggestions.

Dead short

If the other brake and turn lights are working the brake light and flasher units are ok . With a test light check at the bulb holder terminal and bulb holder body, test light should glow ,if not check from terminal to a metal part of panel away from the light body . If test light now glows the brake light body has a bad earth if the test still not glowing the power cable to the light is broken.

Well the brake light and turn signal circuits are on two different fuses, but they both go thru the turn signal switch.
So I would start by checking for power in and out of the turn signal switch for each circuit.

Yes, it does have a flasher, although it may be a combined unit with the hazard flashers relay. So you hear the clicking of the flasher relay? That seems to indicate the relay is working properly. Have you checked the bulbs and the turn signal fuse? Any turn signal bulbs light up anywhere, front or back?
How about your brake lights, do they work? Your car may have separate, stand alone turn signals in the rear, but many American cars use the same bulb and same filament on the bulb for the brake lights and turn signals. If your merc is like this and the brake lights work, then the bulb must be good.
Turn on the hazard flashers and see if all bulbs work and flash at each corner of the car. This would be the same bulb as for the turn signals. If they work, it could be a bad turn signal switch, may even be the flasher relay somehow malfunctioning, and in a few cases, a bad hazard switch can affect the turn signal switch. Check fuses and bulbs first. If you have any type of body control module that controls lights and other accessories, you may have to investigate that. I know I'm not being very helpful, just throwing out a few suggestions. Good luck.

replace your flasher, it controls both turn signal, flashers also brake circuit runs througth.

Fuses and bulbs OK, but wires? Additionally I suggest keep in mind that turn signals work with FLASHER devices (two independent) on 1993 Buick Skylark..

Application: Turn signal
Flasher is located: Front seating area, driver side, under dash, driver side of steering column, mounted on support bracket

Application: Hazard flasher
Flasher is located: Front seating area, driver side, under dash, above kick panel, mounted in top of convenience panel

Hope this helps (remember to rate and comment this answer).

I think I'd check the brake light switch. It may be a switch/button that touches the arm of your brake pedal. It may be stuck, broken, or out of adjustment.

Next check for a bad/broken ground coming from the bulbs in back.

My next guess would be the turn signal switch. Unless the technology has changed, the power for the brake light goes to the switch. When you turn on the turn signal, the power to that brake light would be disconnected and substitutes the turn signal flasher circut.

Let's hope it's the pedal switch.

Do the lights blink with the turn signal?

IF THE TURN SIGNALS STILL WORK IN THE FRONT, THAT MEANS THE FUSE & THE FLASHER ARE OK. IF THE SIGNALS DON'T WORK AT ALL CHECK TURN SIGNAL FUSE & STOP / BRAKE FUSE. ARE YOU SURE THE CORRECT BULBS ARE BEING USED?

Did you actually check the bulbs? I believe your brake lights, signal lights, hazards all use the same bulb for each side.

Your brake lights may be your brake switch just above your brake pedal.
The signals could be your electronic flasher module (EFM) located under the dash near the steering column.
Your hazards may be affected by the EFM, but not likely and the switch for your hazards may be faulty

I have a 2001 Ford F150, my brake lights dont work. Ive replaced the bulbs, checked the fuses,and the brake switch on side of the brake pedal was replaced. I still dont have any brake lights. My third brake light works fine, along with my running lights,flashers, blinkers.