Mix 1 liter of white vinegar, 1/4 cup of baking soda and 1 tsp. of dish detergent in a bucket, then pour some of the mixture into a spray bottle. This mixture will start to dissolve the skunk oils once it makes contact with the suitcase's fabric.
Mist the entire surface of the suitcase, especially where the odor is strongest. Let the cleaning mixture sit for a few minutes. Dip your scrub brush into the cleaning mixture in the bucket, then scrub the surface of the suitcase. Make sure that the area with the strongest smell has been thoroughly covered with cleaner. Repeat this step until the smell is no longer present.
Rinse off the suitcase. Take the suitcase outside and rinse the cleaning solution off thoroughly with a garden hose. If you don't have a hose, take the suitcase to a self-service car wash and rinse the suitcase with their hose.
Spray the suitcase with a deodorizing spray to remove any traces of the skunk smell that remain. Spray the suitcase well in advance of using it to pack your clothes for a trip or after storing it for long periods of time.