Can I use the nba logo, team logos, players names and show results and stats in my open source NBA application?

Not without permission.

I agree with the previous answer. You need to obtain NBA's prior written permission to use their and the teams' logos.

As previously mentioned, you will need permission from the NBA to use the NBA logo or other team logos. You should contact local counsel who may be able to help you locate a contact in the NBA licensing department to answer this inquiry, for example.

Whether your company's proposed use is permissible is a legal question and I agree with others that you should contact legal counsel. Most attorneys provide free legal consultation so please do not hesitate to contact us. Here is general information about NBA's terms of use that will give you a fair idea of why an attorney is required to specifically guide you on what is permissible and impermissible by the NBA. You should not use NBA logos, team names or website material without proper clearance. http://www.nba.com/news/termsofuse.html

You can structure an application that contains scores, statistics and commentary (which are protected by the First Amendment and fair use doctrines), but you cannot use NBA logos, team logos, or player photographs (unless you took the photograph and obtained permission from the player) without permission of the various right-holders. You should not even think about pursuing this project without retaining intellectual property counsel to advise you on how to minimize the risk that you will be sued for infringement. The NBA is notoriously aggressive in enforcing its IP rights, so you need to be very cautious--there is no way for you to safely pursue this without retaining and working closely with experienced IP counsel.