Air carrier Flight Attendant reported a foul smell in the cabin while boarding the aircraft resulted in rejecting the aircraft.

Narrative

I would like to start by saying the most disturbing thing to me was when a new departure time was posted for several hours after the original flight. We had moved our passengers to 3 different broken airplanes at 3 different gates and finally posted another delay at almost XA:00am for XD:00am. The board at the gate changed to XD:00am but there was not an agent there to talk to these people. They were extremely upset and I don't blame them. The number 1 [Flight Attendant] and I were released but we stayed to talk to the passengers. There was a passenger on full oxygen and needed to be in ZZZ1 for her dialysis treatment. Many passengers that wanted answers. The first airplane the pilots had asked for a new plane due to the APU being broken; but were told there weren't any other aircraft available. So it was around 85 degrees. They hooked up the air cart to cool the plane down. The agents were bringing temperature guns down to determine when it was cool enough to board. We started boarding and I started smelling a locker room dirty sock smell. I asked the 1 [Flight Attendant] and he said he smelled it but thought it may be the oven. I called the 2 [Flight Attendant] and she said she didn't smell it but her sense of smell isn't that good. I told the Captain. He asked me to walk through the cabin. I walked through and it was even stronger in the middle. So we deplaned the people and the front end called Maintenance. They came out and they smelled it as well and decided to take it to the hanger. Then they gave us another airplane and the First Officer (FO) did the walk around and discovered that there were multiple bent blades on the engine. Called Maintenance again. They decided to ground this plane as well. (I did find out from the union safety rep that this plane had been already refused by another Captain.) Then they sent us from one concourse to another and gave us our 3rd plane. The Captain told us that this plane had already been refused by another captain so he did the walk around and found bent blades in the engine as well and called for maintenance for a 3rd time. At this time we were released because we were illegal for a XD:00am departure.Suggestions: I am writing this because at the end of the day it is my job to be there for our passengers for safety and service. I do love my job and it broke my heart to see our passengers sitting at the gate without any Company representative to help them.