Two years after Republicans swept away four Ohio Democratic incumbents and seized control of the U.S. House, Democrats are hoping to win back at least three seats this November, which would give the party control of seven of 16 congressional districts.

The party is also hoping Democrat Sharen Neuhardt somehow manages to defeat incumbent Rep. Mike Turner, R-Centerville, in the new 10th district which represents all of Montgomery and Greene counties and part of Fayette.

Just as Ohio figures into the presidential race, it has a key role in the battle over which party controls Congress. Although it may be difficult for the Democrats nationally to win the 25 seats necessary to topple House Speaker John Boehner, R-West Chester Twp., they are poised to spend millions of dollars in an effort to oust Republican incumbents Jim Renacci of Wadsworth and Bill Johnson of Marietta.

They also believe they have a chance to defeat Republican Bob Gibbs of Lakeville, particularly if President Barack Obama rolls up a strong victory in Ohio over Republican presidential nominee Mitt Romney. Boehner is unopposed and Reps. Jim Jordan, R-Urbana, and Steve Chabot, R-Cincinnati, are expected to win easily. Turner, too, is a heavy favorite, but Neuhardt has launched a spirited challenge, unveiling her first television commercial last week.

Former Democratic congressman Zack Space of Dover said three of the races “are competitive and the Neuhardt-Turner race could be competitive. If the Montgomery County vote comes in, Sharon Neuhardt has a shot,’’ Space said.

To Republicans, the Democrats are engaging in wishful thinking. Barry Bennett, a Republican consultant in Washington, said Democrats are “still smoking the funny stuff from Charlotte. If they spend a dime in Ohio, it’s wasted money. So spend all you want.’’

It will be the first time candidates have run in the new districts drawn up last year by the Republican-controlled legislature. Because Ohio’s population has not grown as fast as many southern states, the legislature had to eliminate two seats, giving the state just 16.

Based on voting patterns in past elections, Republicans hold the edge in 12 of those districts, including in the 10th.

Turner, elected to the House in 2002, rolled up comfortable re-election victories in his old district, which included parts of Montgomery and Warren counties and all of Highland and Clinton counties. During the last round of redistricting, Ohio Republicans folded Turner into the same district as Rep. Steve Austria, R-Beavercreek. When Austria chose not to seek re-election, Turner’s GOP nomination was assured.

“Southwest Ohio knows my record of fighting for Wright-Patt, growing new and innovative jobs in the region and as being a leader,” Turner said in a released statement. “When I travel throughout the community I hear directly from voters that they believe our government needs to focus on reining in spending and on job creation. My work and experience are focused on the issues important to our community.”

Neuhardt, an attorney from Yellow Springs, hopes to mount a stern challenge. She lost to Austria by 16 percentage points in 2008, but Austria’s old district was much more Republican than the new Dayton-area district.

She has about $200,000 in campaign money to finance her race and is airing a biographical commercial on Dayton TV stations. Michael McGovern, a Neuhardt spokesman, said that “we’re excited to be up and introducing Sharen to voters in the Miami Valley. We’ve had the resources to run this campaign.’’

Unless the Turner-Neuhardt race gets close, Ohio’s most spirited battle will probably be in northeast Ohio between two incumbents — Renacci and Democrat Betty Sutton of Copley Twp. When Ohio Republicans eliminated Sutton’s district, she opted to challenge Renacci, a first-term Republican elected in the 2010 sweep.

They are deeply divided on the same issues that have created such a furor in the presidential race. Sutton voted for the $787 billion economic stimulus package in 2009 that Renacci said “drove up our debt.’’