With Bay Area home prices at levels not seen in nearly five years, the communities hit hardest by the housing crash are starting to boom again.

From Oakley and Antioch to East Oakland, East Palo Alto and East San Jose, all-cash offers and free rent for a month for sellers are sweetening bids as a swarm of move-in buyers and investors compete for a relatively small number of homes for sale.

"These are the areas seeing the biggest pops," said real estate economist Ken Rosen of the Rosen Consulting Group in Berkeley, although "every place where inventory is tight, prices are moving up."

Some wealthy neighborhoods have already recovered from the crash. Now it's the lower end's turn, although it has a longer climb back.

Antioch's median sales price of $230,000 in the first quarter is up 27.8 percent from a year earlier. East Oakland's median sales price of $158,000 rose 51 percent in that same time, as low-priced foreclosures dried up.

East San Jose peaked at $660,000 in 2007 and fell to $317,000 two years later. In the first quarter of this year, the median price was $415,000 -- a gain of 25.8 percent from the first quarter of 2012.

When Sharon Vaca and her husband moved to Oakley several years ago to take care of her ailing father in his home, the neighborhood was riddled with foreclosures and lawns that were covered with weeds. But that gradually changed.

"Slowly but surely, all the houses on our block are really full, and (it's) looking like a nice neighborhood again," she said.

That prompted the Vacas, who stayed on after her father died, to finally sell the home. It went for $30,000 more than the asking price to a move-in buyer who paid cash. The buyer is letting the couple stay in the house while they look for a place in Fairfield.

"I couldn't believe how many offers we got," Sharon Vaca said. "We ended up having 22. We were like, 'Oh my goodness.' "

The Vacas' broker, Bryce Ellsworth of Windermere Ellsworth and Associates in Brentwood, said in the past month or two, "there has been a huge price difference. The supply is very low. We're in an extreme seller's market."

That's because the inventory of homes for sale is down in many places, about 50 percent in East San Jose, 55 percent in Brentwood, 60 percent in Antioch, and 57 percent in Richmond, according to ZipRealty.

So buyers are snapping up properties as quickly as possible. In Antioch, 68 percent of the homes for sale are in contract in 14 days or less, with 58 percent of them all-cash sales, according to data compiled by the real estate company Redfin. In Brentwood, about half the homes for sale are snapped up in less than two weeks, and the figures are similar for Richmond and East San Jose.

"It's bounced back a lot faster than anyone expected," said Janine Epstein, a teacher at Foothill High School in East San Jose who has been outbid several times. "It's bounced back at high speed."

David Giambruno, a San Jose real estate broker, said inventory is gradually beginning to rise, but that as long as low interest rates draw out lots of eager buyers it will continue to be a seller's market.

How long this will last is unclear. Economist Rosen said prices can't keep going up at this pace, but an additional 20 percent increase will bring out more sellers.

Right now, investors are still taking advantage of relative bargains and looking forward to the profits to come.

Carol Nurmi, a San Jose tech engineer, recently bought a home in Union City as an investment, beating out 14 other bidders.

Union City is not as impacted as many other communities, but "there are a lot of lower-priced properties that are available," she said. "There's a lot of competition, however."

Nurmi, who has taken time off from work to assist her ailing mother, said, "Real estate right now is very good for me. I like to take a home that needs work and beautify it, reconstructing it in way that is livable and pleasant, either for renting or resale."

In East Palo Alto, sale prices average 7.5 percent more than the asking price, according to Redfin.

An East Palo Alto condominium, listed at $210,000, drew three offers and sold for $245,000 recently, said Coldwell Banker agent Arn Cenedella. "A year ago, you couldn't give those units away for $175,000. They are little one-bedroom units."

Contact Pete Carey at 408-920-5419. Follow him at Twitter.com/petecarey.