Is it better to go for maintaince service with dealership or privately owned

Depends on how much money you want to spend and how much you know about either place If you know of a privately owned shop that you feel good about that's where i would go.Most of the time you get more personal attention and can save some $.

it really depends on your area i would get a friend to rec a good repair shop

I work at a Honda dealership , HOWEVER....I would STRONGLY recommend supporting small business!!!!!!!!! With that said I would also recommend factory fluids and parts. May cost a little more for the independent to get , but it will make your Odyssey MUCH happier (& that includes oil filters).