Nordtveit's low shot took a deflection off Sammy Clingan's heel to beat keeper Lee Camp just before half-time.
Substitute Elyounoussi produced a fine shot on the turn in the 87th minute and another replacement Ruud made it 3-0 to Norway with a fine volley.
Northern Ireland started well but rarely threatened in the second half.
Before the goals, home skipper Steven Davis, Martin Paterson and Gareth McAuley were all thwarted during a frantic goalmouth scramble.
It means Northern Ireland have won just one of their last 14 friendlies.
They started brightly with full-back Ryan McGivern's drive being tipped away by goalkeeper Rune Jarstein.
Northern Ireland were knocking the ball about well and the atmosphere at Windsor Park seemed optimistic.
However, O'Neill's men were unable to make the breakthrough and were hit by Norway's opening goal in the 44th minute.
Aaron Hughes half-cleared a corner as far as Nordtveit, whose shot beat Camp via the unfortunate Clingan.
Grant McCann, a half-time substitute, had a decent crack at goal soon after the break with his 25-yard drive being tipped away by Jarstein.
Paddy McCourt came on with just over 20 minutes to go, replacing Shane Ferguson.
The Celtic man was watched from the stands by club boss Neil Lennon, returning to the ground where he was once barracked by his own fans on international duty.
David Healy then came on as a substitute to become Northern Ireland's most capped outfield player on 92, passing Mal Donaghy.
Elyounoussi extended the visitors' lead three minutes from time when he beat Camp at the near post with a fine shot.
Ruud's superb injury-time volley made it 3-0 despite the Nottingham Forest keeper getting a strong hand to it.
Northern Ireland: Camp, McAuley, Hughes, Jonathan Evans, McGivern, Corry Evans, Clingan, Davis, Ferguson, Shiels, Paterson.
Subs: Mannus, Hodson, McGinn, Healy, McCann, Duff, McQuoid, McCourt, Carson, McGovern.
Norway: Jarstein, Hogli, Rogne, Demidov, Riise, Henriksen, Nordtveit, Grindheim, Pedersen, Abdellaoui, Huseklepp.
Subs: Pettersen, Reginiussen, Elyounoussi, Ruud, Jenssen, Braaten, Berisha.
Goals from Havard Nordtveit, Tarik Elyounoussi and Espen Ruud ensured Michael O'Neill's first match as Northern Ireland boss ended in defeat.