Apologies, it seems none of us has any direct knowledge so far
When there is no info on here about a country, you can use the website gsmworld. Choose the country on the Coverage Maps page, which gives a list of networks there
GSM Coverage Maps | Sri Lanka
Then the Network Information link goes to a page which includes a link to the network's own website, thus they are
:: Airtel :: Srilanka
Dialog
..:: Hutchison Telecommunications Lanka (Pvt) Limited ::..
Mobitel - National Mobile Services Provider of Sri Lanka
Tigo - Sri Lanka
Hutch and Tigo do not have 3g. A quick look shows there is some mobile broadband, and Dialog certainly has it available as prepaid, with for example a week's browsing (2 GB or 24 hours total time) for 400 Rs ~ €2.50, and it seems you can use the same SIM for phone and web use