Air benders can fly and remove the air from people's lungs, water benders can control and rip out the blood from someone's body (Not to mention 70% of the earth's surface is water) and earth benders control the ground beneath people's feet and can construct massive rock structures
fire benders just shoot fire
Yes, air benders have the potential to fly and remove air from people's lungs. Yes, water benders can blood bend. Yes, earth benders can control ground and have the potential to control metal and even lava bend. As said earlier, fire benders can lightning bend.
However, you should realize that Zaheer is only the second air bender in the history of their world to be able to fly. Right before the air benders went extinct, most thought the ability to fly was a myth. Since the air benders were peaceful nomadic groups, they only used their bending for defensive purposes at most. They wouldn't dare air bend the air from people's lungs. In the case that there were a few bad air benders willing to do so, I would doubt they could have the focus to do that to an entire army. In the worst case scenario, they would be zapped by lightning and die on the spot.
Water benders can only blood bend during the full moon. Yakone was the first one known to be able to do so without a full moon, but that was long after the war ended. Generally, water bending was used for defensive purposes, but some can use it effectively for offense. Then again, the fire nation sent many warships, and the army was much bigger than the tribes we have seen. The Northern Water Tribe seemed to be the only ones able to defend themselves, but I doubt they alone had the power to fight back. Also, lightning bending would be very useful against talented water benders. Look at what it did to Ming-Hua.
Fire benders never really took control of the Earth Kingdom until Azula took Ba Sing Se. That was basically 100 years after the war started. So you are right that earth benders are powerful enough because they mostly stayed unconquered for a hundred years besides having some land taken. They didn't have metal bending until Toph invented it.
In the end, while the Fire Nation did wipe out air benders and conquer some territory, I don't think they conquered that much considering the Earth Kingdom still existed for those hundreds of years as well as the Water Tribes still existing. All the special overpowered bendings didn't become prominent until after Aang woke up. The Fire Nation was able to conquer and gain territory because of technology, numbers, and resources. Also, the other benders couldn't defend themselves with OP abilities because they didn't know about metal bending, blood bending, and flying. Also, most air benders are not violent enough to bend the air out of lungs.
Edit for correction: Yeah, the Fire Nation did take most of the Earth Kingdom minus a few strongholds and the Northern Water Tribe. They had 100 years to do so with the economic, technological, and military power that the others lacked.