Dental Floss
Sticker Shock, Goo be Gone, or Rubbing Alcohol
Plastic Scraper

Use the dental floss to get behind the badges and separate the glue from the paint and the badge.  Work first from the top down around the side and then from the bottom up.  I pulled about a 3 foot piece out and tripled it up.  The reason for working both ways on the H badge is the peg holes that go into the body.

When you've worked the floss all the way around the badge lightly pry it up with your finger nail and pop it out of the peg holes.

Proceed to do the same thing to the odyssey badge, but instead of working from the top and bottom work from the left and then from the right.  You will only be able to get about 1/3 of the way on either side.  Once you have done that slowly pry the rest of the badge up with your fingers from the peg hole.  It's very easy to snap so be careful if you want to hold on to it.

After you have removed both badges use something like sticker shock, goo be gone, or rubbing alcohol to remove the glue left by the badges.  You can rub it really hard with a paper towel or cloth after letting it soak, but generally there is still some residue left behind.  You can also use a plastic ice scraper to gently remove the rest of the glue with the use of the adhesive remover.  I didn't completely remove all the glue on mine since I was working on a spare hatch that I plan on filling the holes in and repainting.

Something to note is that if you have the Isuzu Oasis it does not have the peg mounting holes, so once the badges are removed and the glue cleaned up there are no peg holes to be filled in.

Here's the back of my Oasis after removing the badges: