Can the majority leader of the house be impeached ?
It's a constitutional office.
Boehner can be swept out on a single vote ~ quite comparable to a vote of confidence in a parliamentary system only we don't call it that.
Henry Clay had his terms cut short twice, Andrew Stephenson was cut short, MIchael Kerr, Henry Rainey, Joseph Byrns, William Bankhead, and even Sam Rayburn were cut short before the end of their terms.
I suppose some of this was because of death or disability. But there's nothing to stop the majority party from withdrawing its support and bringing down a Speaker.
Impeachment never occurs against House members, Speaker or not.
It occurs against executive branch members and federal judges.
In the House, members CAN be expelled from the House and various lesser punishments such as a reprimand.
Leadership has to run for its positions and can be voted out just as they were voted in. But another member has to be voted into the position instead. They only stand for leadership elections at certain times, though, not ALL the time.
LOL, I had to do a double take. Where you said "impeached," I originally thought you said another word, that also begins with the letters "I-m-p". Maybe that is what people would call a Freudian slip.