I have the same van. 2005 EX-L. And the same issues. Kicking myself now because I didn't even think about checking the warranty for the battery and the hydrolics. I've only had to replace my battery once though, about a year ago.
The rear hydrolics we replaced about a month ago. DH just bought the parts and did it himself. Took less than an hour and under $100.
I hate vans. I hate being the minivan mom. But I LOVE
my Odyssey. My van has been to Disney from GA and VA 8 times, it visits GA from VA every year, it drives all over the state for gymnastics competitions, it visits TN once a year for gymnastics camp. It's wonderful. My dh has a 4 door sedan. My van has been get up and go than his "you want me to do what?" car does. I've been in one accident in it. The fall of 2005 (I got it in Feb) I was changing lanes and some jerk decided he didn't want a van in front of him and decided to gun it and try to pass me. He ended up sliding down my entire passenger side. His car was a mess. His bumper was hanging off, he took off his side mirror...Did a fair amount of denting to my doors and the only thing needed was to replace the panals. No one inside hurt in any way.
If I were to get another van - I wouldn't hesitate to get another Odyssey.