Silver and gold do not react with oxygen even at high temperatures.but yet silver and gold turn to some other colour after a few years or months. how is it so?

Yes Silver and gold do not react with oxygen even at high temperatures as they are less reactive and are placed below the reactivity series. Hence they are called noble metals. 

But silver fades after some months or years due to its tendency to react with sulphur in air forming their sulphides. Silver reacts with hydrogen sulphide in the air silver forms silver sulphide (Ag2S) which is responsible for the black coating on silver.

But gold pretty much doesn't react with almost anything it normally comes in contact with and stays untarnished. Gold is unaffected by air, water, alkalis and all acids except aqua regia (a mixture of hydrochloric acid and nitric acid) which can dissolve gold. Gold does react with halogens.