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When I say "Thanks" to one of my friend,he replies me by saying ''Anytime".
Doesn't its an odd reply?
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No this is not an odd response. A lot of Americans might say this. It's just very informal and it means that he/she is glad to help at any time. But I would write it as 2 words, any time Emotion: smile
What should we say formally?
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Formally, just say "You're welcome" or "Don't mention it" but you only need to say one of those in the most formal circumstances, as a sign of respect; for example, if you don't know someone, or if you're speaking to a business executive or someone who is much older than you.
I've found that "Any time" as a reply carries a certain tone of familiarity, in addition to being casual. Of course it can depend on whether one stresses the first word or the second.
When said casually to a stranger, it implies, "Let's do it again sometime."
(At least that's the way it seems to me.) [6]
When it's said to a friend, there's usually no double meaning.

- A.
"You're welcome" or "Don't mention it"These I know.
I need something that looks more attractive.
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My pleasure.
It was my pleasure.
Glad to do it.
You bet.
Happy to help.
I'm glad it was helpful.

(I really hate "no problem.")