Can we get discount on traveling in group of 3 from Stansted airport to London by train?

No.

you'd need a much bigger party than 3 to get any group discount

If you have three people then I would think it would be worth it to take a taxi. It's a real pain to transfer to the underground and get to your hotel.

Yes. Most train companies running to London now offer 3 tickets for the price of 2 except during the morning rush hour. Check with Stansted Express at www.stanstedexpress.com. In any case they certainly offer discounts for tickets purchased in advance, or if you have a railcard or are travelling with Easy Jet

You can use railcards on the express trains so if any of you are children then you can use a family and friends railcard, if any are over 60, you can use you freedom pass (if it's issued in London) and if any are under 25 you can use a young persons railcard.

If you book your tickets online you can save £2 per person:

https://www.stanstedexpress.com/content.asp?SID={C0F5C3C7-7B9E-473A-B2FD-866D89F47E85}&pageid=111

Paco, David S and Carrie S all make good points.

There isn't really a short definitive answer.
Where in 'London' do you need to get to? What time of day? What age are the people?
Personally I'd get an ordinary train to Tottenham Hale, and then the Victoria line on the tube, but that's because my final destination is a short walk from Pimlico tube station.

Come to think of it, unless you want to go to the City (financial district), Liverpool Street Station isn't a great place to be anyway.
(The architecture is great, but the transport connections aren't.)

Look at a tube and rail map, decide how far you are willing to carry any luggage you have, but remember the 'Stansted Express' is far more expensive than 'normal' 'stopping' trains passing through Stansted.

http://www.tfl.gov.uk/gettingaround/1106.aspx#

http://www.thetrainline.com/default.asp?href=ppcg_brand&WT.srch=1&WT.mc_ev=cli ck&gclid=CKnj3qC2wZkCFRWRZgod4B4evQ

might help - good luck!