I wouldn't avoid low doses of Vitamin K. Vitamin K provides other benefits, aside from promoting clotting, and it is supposed to also help stabilize your INR. The thing with K is that you can adjust your dosage to account for the effects of Vitamin K, and still go on with a steady dose. You don't need to COMPLETELY avoid Vitamin K, as long as you are fairly consistent with the dose of K and have adjusted your warfarin to account for its effects.
As far as Vitamin C is concerned -- I'm not sure of an effect on INR. I used to take Quercetin, which is related to, or supposed to be a form of, Vitamin K, and it seemed to fool the InRatio into giving abnormally high readings. I avoid quercetin. but probably get Vitamin C in my Naked Juice and daily pack of vitamins.
As long as you test regularly, and make minor dosing adjustments IF NECESSARY, you should be fine with Vitamin C (and with low dose K).