I have no experience with the Sequence and little experience with the Structure.
I do have some experience with the Odyssey. I have about 50 miles on my pair. I love them!
The shoe has plenty of cushioning without being mushy. I used to run in Brooks Transcends. They seemed to be mushy and a little bit to cushioned. I liked the first version when it wasn't as soft. The second version became much more built up and a lot softer. That's what prompted my switch to the Odyssey.
The Odyssey doesn't feel stiff or mushy. The midfoot and forefoot have very good flex and is very responsive even for a high cushion shoe. The heel is stable enough. Looking at the shoe it comes off as a clunky and overly stable motion control shoe. That couldn't be more wrong. I feel like it runs like a nice neutral shoe with good stability for those who need it. That being said a neutral runner should not wear this shoe. The only downside i have with this shoe is the forefoot rubber. It is very grippy but that makes it wear fast. I do think the rubber will last to the 400 to 500 mile mark but it will be worn down quite a bit and the cushioning feels very durable to me so far.
If you're a person that has been running in a stability shoe I highly recommend the Odyssey if you want a little bit more cushion without sacrificing a shoe that feels like it can go fast once in awhile.