The NFL teams presumably own trademark rights to their name and trade dress (including their colors) for various goods and service. You can look up the classes they've trademarked at the uspro site linked below.
Generally trademark fair use law lets you refer to the teams in a nominative way to identify them, but doesn't allow others than the rights holders to trade on those marks by using them mofre than is necessary to identify them, and you must give proper attribution to the rights holders. It's a tricky area, so before you use others' marks, you should consult with a qualified lawyer about your intended use.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Use them on what? As has been pointed out - this can be a tricky area of the law and the NFL and the respective teams are VERY protective of their intellectual property rights. You should consult with an attorney before proceeding.