Read MoreOil extends gains after EIA data
Oil majors like Exxon and Chevron were sharply higher, as were energy ETFs, like Market Vectors Oil Services ETF OIH and the Energy Select Sector SPDR Fund XLE. Transocean, Diamond Offshore, Halliburton and dozens of other names in the sector saw gains of 3 and 4 percent.
Read MoreTrying to pick a bottom in energy stocks
Analysts say it could take a change in stance by OPEC for the oil market to see a bottom. "I don't think we can determine that at all yet. In the last four months we've seen rebounds in prices from $3 to $5 and the market is still headed lower," said Gene McGillian, analyst at Tradition Energy.
"Until we get a sign these things that were driving us down are changed, we're still going to go lower," said McGillian, who said short covering was a big factor Wednesday.
Fadel Gheit, senior energy analyst with Oppenheimer, said the market may be getting close to a bottom.
"All the oil stocks are rising because people believe oil prices have bottomed. That's a second strong day in a row. People think if it repeats three times then the thing is real," said Gheit.
One reason that analysts expect oil prices to remain low is that supply continues to increase and will into the first half of next year. Newer U.S. wells are expected to continue to produce several hundred thousand more barrels a day next year, down from the million barrels expected when prices were high.
U.S. oil production grew last week to 9.14 million barrels a day from 9.12 million the week earlier.
Even Russia, badly burned by lower oil prices, could also put more onto the world market. New rules on refining tariffs could result in more product exports starting in January, said Andrew Lipow, president of Lipow Oil Associates. Russian consumers could also require less fuel if the economy continues to tank, and that could put more oil on the world market.
Citigroup energy analyst Eric Lee, however, said Russian output could go either way next year, depending on how much the financial crunch is hurting production. But he does agree more U.S. oil will make it to market and also oil from other places, like Kurdistan and potentially Iraq.
"I think there will be a sub-$50 (for WTI) in our future ... I think the low for this market will be late February/March due to the slack demand period. The refineries will be in maintenance for turnarounds," Kilduff said.