If I understand you right, with the key on when you turn the left blinkers on the left blinkers do not come on but the right ones do---but are solid not blinking? And when the key is off and the turn signal lever is in the neutral position the right blinkers are still on but not blinking?? If this is the case then the problem is probably with the turn signal lever-----but even then the lights should be off with the turn signal lever in the neutral position and the key off. Maybe you should clarify the symptoms some more.

Go to reputable auto tech only.

You have a burned out light bulb on that side of the car. Front, side, rear. Check them all. One of them isn't lit up when you are signalling.

Check the bulb in front and on back of right side. Sometimes a bulb will blow and the filament falls on other filament and thats what happens. 99% sure thats the problem.

Something is broken, maybe the indicator switch assembly. Needs replacement.

If all the globes light up, you have a faulty flasher unit.

I drive a 94' acura legend. I saw the the right side of my car's lights are on. The rear right shows a orange light and on the dash the right signal does not blink and stays solid. even when the car is off both lights are on. i tried turning the left but nothing happens just a solid right light and a orange light from the back.