I have never sent the same transaction to multiple people. When I send money to a single person, say I pay 0.0004 in fees. Can I send money to multiple people in the same transaction and pay just one fees for the entire transaction ?
If so, then is there an online wallet which supports this feature ?
No, you can't send Bitcoin to multiple addresses with the same fees used for a single transaction, because your inputs and outputs data size would be bigger (obviously), but paying in a bulk reduces the fees drastically rather than paying one at a time.
Also, I don't think there is an online wallet that would support such feature. There are four wallets that I know support this feature: Electrum; Bitcoin Core; Armory; and Blockchain.info.