Firstly the deposited tartar cannot be removed with home remedies.
The thing you can do to remove the tartar is go to your nearest dental clinic and get a simple procedure of Scaling & Polishing(Simple cleaning of your teeth and removal of tartar with ultrasonic machines ).
This procedure will not only take care of your tartar it will also prevent any further gum diseases the deposited tartar could have created.
This is how it went--Unproper cleaning of teeth-- Deposition of Tartar -- Bleeding of gums --Bad Odor -- Pain
This is how it will go after Scaling -- Proper self cleaning of teeth-- No Deposition of Tartar--Clean Teeth & Healthy Mouth
Next Steps
Go for proper scaling and polishing procedure and prevent your teeth from further damage. Also check for any other medical history you may have .
Health Tips
After Scaling, brush twice daily with proper fluoridated toothpaste, floss everyday, use mouthwash and change your brushing technique if faulty.