GLOBAL MARKETS-Stocks and oil prices gain as Brexit nerves settle

* European stocks up broadly, banks gain

* Bonds strong on talk of easier monetary policy

* Sterling recoups 4 cents; FTSE closes at pre-Brexit levels

* Oil jumps on U.S (Other OTC: UBGXF - news) . drawdown, looming strike in Norway (Adds U.S. markets open; updates prices; adds Moody's quote, European banks index; changes dateline from LONDON)

By Hilary Russ

NEW YORK, June 29 (Reuters) - Stock markets around the world rebounded for the second day on Wednesday as fears about last week's Brexit vote eased and investors wagered central banks would ultimately ride to the rescue with more stimulus.

Oil prices rallied and Wall Street was sharply higher, turning positive for the year. Britain's FTSE 100 recovered all its post-Brexit losses to close at the highest level since April.

UK and European banks, a focus of concern since Britain shocked global markets by voting to leave the European Union, extended a recovery from two days of trading that had knocked almost 40 percent off shares in Barclays (LSE: BARC.L - news) and RBS (LSE: RBS.L - news) .

An index of major European banks was up for the second straight day, but the gains could not come close to offsetting losses in the first two trading sessions after the referendum. Still, stock markets in Frankfurt, Paris and London all gained more than 2 percent.

"While the initial panic from Brexit appears to have eased, a huge amount of uncertainty remains, which could continue to weigh on sentiment for a while," said Craig Erlam from online brokerage Oanda.

The S&P financial stocks index, which was hit the most since the referendum, was up 1.13 percent.

The Dow Jones industrial average rose 216.17 points, or 1.24 percent, to 17,625.89, the S&P 500 gained 27.9 points, or 1.37 percent, to 2,063.99 and the Nasdaq Composite added 73.82 points, or 1.57 percent, to 4,765.68.

Sterling, the other big victim on Friday and Monday, was last up 1.4 percent at $1.3522 against the dollar to recover a full 4 cents after Monday's 31-year low.

Markets face a prolonged period in limbo while a new UK prime minister is selected and officials come to grips with the possible scenarios for Britain's departure.

At the heart of the recovery are expectations that major central banks will go easier on monetary policy in anticipation of another hit to global growth from Europe.

The U.S. 30-year Treasury yield approached record lows in a scramble for long-dated bonds on bets of more unconventional stimulus measures from major central banks.

"There are very reasonable expectations from central banks globally, especially from the U.S. Federal Reserve, the ECB and the BOE, to provide more liquidity, guidance and clarity to support markets," said Stephen Woods, chief market strategist for Russell Investments in New York.

The first Federal Reserve policymaker to comment since the vote, Governor Jerome Powell, said Brexit had shifted global risks "to the downside", reinforcing expectations the Fed will not hike U.S. rates this year and could even cut.

"The Fed is going to be slower to begin raising rates again," said Mark Zandi, Moody's Analytics' chief economist.

Oil prices jumped after a larger-than-expected weekly drawdown in inventories, adding to its rally on fading concerns over Brexit and a looming strike by Norwegian oil and gas field workers.

U.S. crude oil futures were up $1.23 cents at $49.06, while Brent crude rose $1.18 cents to $49.76.

Gold (Other OTC: GDCWF - news) was firmer around $1,323.50 an ounce, off a low of $1,305.23 touched Tuesday. (Additional reporting by Patrick Graham in London; Sam Forgione and Barani Krishnan in New York; Wayne Cole in Sydney and Yashaswini Swamynathan in Bengaluru; Editing by Jeremy Gaunt and Nick Zieminski)