Is it possible to use the Web3.js API methods to interact with Eris blockchain? If yes, what should I pass in as the argument for setting the web3 provider?
Since Eris is a permissioned blockchain, you will have to make the permission-logic inside your api layer to make it work. Eris is technically a fork of Ethereum with improvements. source. Web3 should work out of the box, but i am not sure whether they internally disabled it or not.
But there is eris-db.js
Take a look at the examples