Click here for a map of parking in Odense.
The site is in Danish but should be quite easy to understand. The colours green, yellow and red indicate whether or not there are any available spaces - blue means that it is not part of the automated system, so you will have to take your chances.
On the page it is possible to filter by payment method, so scroll down a bit and choose your credit card to see a list of parking spaces you can choose from.
Please note that practically all information regarding parking and payment will be in Danish and that you will need a credit card in many places. Parking fines in Denmark start at app. 600 DKK, so try to avoid them.