* Four centre-right groups take 96 seats vs 85 needed
* Solberg faces tricky coalition talks with populists
* Conservatives promise tax cuts, better health care
By Balazs Koranyi and Gwladys Fouche
OSLO, Sept 10 (Reuters) - Norway's opposition Conservatives, promising tax cuts and better healthcare, won elections in a landslide on Monday but faced tough coalition talks with a populist party that wants to spend more of the accumulated oil riches and curb immigration.
Led by Erna Solberg, a former girl scout leader who has overcome dyslexia, the Conservatives promise to diversify the economy away from oil, privatise state firms, and reduce some of the world's highest taxes rates to give the private sector more breathing room.
Solberg, 52, will become Norway's second female prime minister, as well as its first Conservative prime minister since 1990. At least the top two cabinet posts - and possibly the top three - are likely to be filled by women.
"Today voters have given a historically strong victory for the centre-right," said a tearful Solberg, nicknamed "Iron Erna" for her tough stances when she served in cabinet between 2001 and 2005. "We will give this country a new government."
Norway has enjoyed rare economic success during the past decade, escaping Europe's economic crisis with little more than a scratch, as its booming offshore oil sector lifted per capita GDP to $100,000 and a huge public sector insulated the economy.
But growth is now slowing, competitiveness is stagnating, and the government's record on critical social services is mixed. Voters have accused outgoing Prime Minister Jens Stoltenberg of wasting a once-in-a-lifetime economic boom.
With 76 percent of the vote counted, the Conservatives, the populist right-wing Progress Party and two centrist parties that campaigned together to oust Stoltenberg were set to collect 96 seats in parliament, 11 more than needed for the majority.
Stoltenberg and his allies collected just 72 seats and the prime minister announced he would step down after eight years and two straight terms in office.
"I have waited for a long time to say this: Good bye Jens!" Progress leader Siv Jensen screamed to cheering supporters. "We will sit down and negotiate a common government platform."
The trickiest task for Solberg, who will become prime minister on her third attempt, will be to tame the anti-immigration, anti-tax Progress party, which will enter government for the first time.
Although Progress has toned down its rhetoric, it is seen by some as too radical for government, and once had among its members Anders Behring Breivik, who killed 77 people in 2011 in a gun and bomb attack targeting Labour.
The small Christian Democrats and Liberals, one of whom will be needed for a majority, are not keen on teaming up with Progress, objecting to its policies on immigration and spending, raising the prospect that Solberg may lead a minority cabinet.
"We will contribute to a change (of government)" Christian Democrat party leader Knut Arild Hareide said. "We've been guaranteeing that a change will take place, and we will keep that promise," he said without committing to entering cabinet.
Norway has a long history of minority governments, which tend to be stable, due at least in part to laws that do not allow for early elections.
"The difference between the Progress Party and the centre parties is big," Johannes Berg, a researcher at the Institute Of Social Research said. "It is possible to make a government but it will be very difficult.
"Progress wants to use more of the oil money than the other parties, their immigration policy is much more strict than the others, they want to tighten the foreign aid budget, which the other parties are against," he said.
Bringing Progress into government could force Solberg to make concessions on spending, taxes and perhaps even make a symbolic gesture on immigration. But any shift is likely to be mild, analysts said.
In immigration, Norway's hands are tied by international treaties, which limit its room to manoeuvre. And the economy desperately needs new workers as unemployment is under 3 percent and a steady influx of workers keeps the labour market from overheating.
But on spending, the next government will have big leeway, as it levies a 78 percent tax on the oil sector, amassing huge budget surpluses and a $750 billion oil fund worth more than 150 percent of GDP.
"The Conservative and Progress parties are in agreement about lowering income tax and wealth tax as well as increasing public sector fees in some areas," DNB, the country's biggest bank, said. "At the same time they have very divergent views on which cuts of taxes and duties should be given priority."
Danske Bank predicted that spending under the new government would rise by up to 15 billion crowns ($2.5 billion) next year, or 0.66 percent of the non-oil economy, a big increase but well within the budget's means.
One of the major sticking points will be changes to the oil fund as both parties want big changes but do not agree on the specifics, with the Conservatives keen to get a broad consensus on any reform to the fund.
Progress wants to break off three smaller funds from the main fund and spend more of the oil money domestically, while the Conservatives have mooted the idea of breaking the fund into two competing funds and do not want to spend as much oil money domestically as Progress.
The parties are likely to find more common ground on privatisation as they argue the state has grown too big. Solberg has said Norway should sell down some of its holding in Statoil and telecoms group Telenor.
Solberg said her party will gather on Friday to appoint official negotiators and the new cabinet will take office after the outgoing government presents the 2014 budget on Oct. 14.