* Oil prices enter bear territory, Brent at 7-month lows
* Investors price in lower inflation, boost long-term bonds
* Asia shares stumble as energy stocks fall
* China stocks seen getting limited lift from MSCI inclusion
* Dollar underpinned, sterling nurses losses after BoE comments
SYDNEY, June 21 (Reuters) - A renewed slump in oil prices to seven-month lows put Asian investors on edge on Wednesday, overshadowing a decision by U.S. index provider MSCI to add mainland Chinese stocks to one of its popular benchmarks.
The slide in energy costs boosted bond prices and flattened yield curves as investors priced in lower inflation for longer, while safe-haven flows underpinned the U.S. dollar.
The spread between yields on U.S. five-year notes and 30-year bonds shrank to the smallest since 2007.
MSCI's broadest index of Asia-Pacific shares outside Japan slipped 0.5 percent, with Australia's commodity-heavy market down 0.7 percent.
Japan's Nikkei eased 0.3 percent.
Oil had shed 2 percent on Tuesday as increased supply from several key producers overshadowed high compliance by OPEC and non-OPEC producers on a deal to cut global output.
The drop took U.S. crude down 20 percent from its recent high and thus into official bear territory, a red flag to investors who follow technical trends.
Early on Wednesday Brent was down another 6 cents at $45.97 a barrel, while U.S. crude futures were flat at $43.51.
The hit to energy stocks saw the Dow end Tuesday down 0.29 percent, while the S&P 500 eased 0.67 percent and the Nasdaq 0.82 percent. E-Mini futures for the S&P 500 were a fraction lower on Wednesday.
The acceptance of some Chinese A shares into MSCI's Emerging Markets Index was seen as a symbolic win for Beijing after three failed attempts. Yet the step is still a small one.
Only 222 stocks are being included and, with a weighing of just 5 percent, they will account for only 0.73 percent of the Emerging Markets Index.
MSCI estimated the change, which does not happen until June next year, would drive inflows of between $17 billion and $18 billion. China's market cap is roughly $7 trillion.
The index provider set out a laundry list of liberalisation requirements before it would consider further expansion.
"We suspect that it will be a long time before this happens," wrote analysts at Capital Economics in a note.
"While China's weighting in the MSCI Emerging Markets Index may ultimately rise to 40 percent or so, this rise is likely to be slow," they added. "The upshot is that any initial boost to equities is likely to be small."
China's CSI300 index had already risen in anticipation of MSCI's acceptance and touched a near 18-month peak last week.
MSCI also said it would consult on adding Saudi Arabia to the benchmark and that Nigeria will remain a frontier market, But it shocked many emerging market investors by failing to upgrade Argentina from the frontier market category.
In currency markets, the flight from oil benefited the U.S. dollar -- the two often move inversely. Against a basket of currencies, it was holding at 97.715 having touched a five-week peak overnight.
The euro stood at $1.1136 after hitting a three-week low, while the dollar was steady on the yen at 111.36.
Sterling was nursing losses at $1.2624. It took a spill after Bank of England Governor Mark Carney hosed down speculation that he might soon back higher interest rates, saying he first wanted to see how the economy coped with Brexit talks.
(Reportig by Wayne Cole; Editing by Eric Meijer)