* Dollar downtrodden after suffering worst year since 2003
* Commodities benefit from dollar weakness, China demand
* Oil prices hover at highest since mid-2015
* European shares squeezed down by currency strength
* Wall Street expected to start 0.3 percent higher
By Marc Jones
LONDON, Jan 2 (Reuters) - The ailing dollar fell to its lowest in over three months on Tuesday, while surprisingly upbeat Chinese manufacturing data ensured there was no serious new year hangover for world shares despite a groggy start for Europe.
Wall Street was expected to get 2018 off the mark with a small gain, with sentiment also helped by news that North Korea had offered an olive branch to South Korea. Kim Jong Un said he was "open to dialogue" with Seoul.
MSCI's broadest index of world shares climbed 0.2 percent, having set scores of record highs and risen by one-fifth in value last year. reut.rs/2zLv6kT
The driver overnight had again been Asia and its emerging markets.
Shanghai blue chips climbed 1.4 percent and MSCI's 24-country EM index jumped to a 5-1/2 year high after the Caixin index of Chinese industry rose to a four-month high of 51.5 in December, confounding forecasts for a decline.
The reading pointed to resilience in the world's second-largest economy even as Beijing cracks down on industrial pollution and engineers a cooling property market.
"Manufacturing operating conditions improved in December, reinforcing the notion that economic growth has stabilized in 2017 and has even performed better than expected," said Zhengsheng Zhong, director of macroeconomic analysis at CEBM Group.
In currency markets, the dollar remained out of favour having already hit a three-month low against a basket of its peers on Friday. That brought its losses for 2017 to 9.8 percent, its worse performance since 2003.
Its pain was the euro's gain though, with the single currency enjoying its strongest year against the dollar in 14 years.
On Tuesday, it jetted to a near-four-month top of $1.2081 as data showed that euro zone manufacturers ramped up activity last month at the fastest pace in more than two decades.
It had already sliced through major resistance on the yen in Asia, reaching highs not seen since late 2015 at 135.45 yen . The rally against dollar meanwhile meant euro bulls were now eyeing the September peak of $1.2092, a break of which would take the currency to ground last trodden in late 2014.
"Forward-looking indicators bode well for the new year," Chris Williamson, chief business economist at IHS Markit which compiled the manufacturing data, pointing to a near record pace of new orders and job creation by euro zone firms.
The pound, Swiss franc and Scandinavian currencies were also up solidly against the struggling dollar.
That combined with a two-month high in bond yields in Germany and Italy, two of the euro zone's biggest debt markets, pushed stock markets in London, Frankfurt and Paris 0.4-0.7 percent into the red.
Carmaker stocks caused the biggest dent, skidding 1.4 percent on weaker new car registrations data from France and forecasts that those in Britain would see as much as a 5 percent drop later in the week.
U.S. traders were gearing up for what was expected to be a steady first session of 2018, having seen the S&P 500 leap 22.5 percent last year but the dollar dive almost 10 percent.
A major hurdle for the U.S. currency will be Wednesday's release of minutes from the Federal Reserve's December meeting, when it raised interest rates. Two policymakers voted against the move amid doubts inflation would accelerate as hoped.
With the market now pricing in a 68 percent chance of a March hike and two hikes for 2018, there will be close inspection to assess just how shaky their confidence is for any pick-up in inflationary trends said Chris Weston, chief markets strategist at broker IG in Sydney.
"That said, the U.S. dollar is underloved and oversold and it won't take much to promote a bout of profit-taking from the shorts."
The skid in the dollar, combined with strength in Chinese demand, has benefited commodities priced into the currency.
Copper dipped back a little on Tuesday to $7,235.50 a tonne, but that follows a rise of 31 percent in 2017 to a four-year top. Aluminium amassed gains of 34 percent.
Gold was 0.7 percent firmer at $1,311 an ounce, after advancing by 13 percent in 2017 for its best performance in seven years.
Brent crude oil futures ended the year with a 17 percent rise, while U.S. crude climbed 12 percent on strong demand and declining global inventories.
On Tuesday, Brent added another few cents at $66.92 a barrel, while U.S. crude firmed 7 cents to $60.48.
Alongside the upbeat China data, factory activity had also hit a five-year high in India and the best in 6-1/2 years in Taiwan.
In emerging Europe, Hungary's Purchasing Managers' Index (PMI) recorded its strongest December on record, Czech data was at the highest since 2011 while Turkey's reading rose for a 10th straight month.
"Some of the PMIs have been really strong and in central/eastern Europe we have seen some of the strongest numbers on record. So it looks like 2017 ended on a strong note in growth terms and that's translating into better sentiment on markets," said William Jackson at Capital Economics.
Additional reporting by Wayne Cole in Sydney and Sujata Rao in London; Editing by Catherine Evans