My sister is incarcerated and is being evicted from her apartment. She asked me to collect her things. Can I legally enter her apt if I have a key?

Until the eviction goes through, yes--as long as your sister still has legal possession of the apartment (i.e. as long as she could enter, were she not incarcerated), she can have anyone else enter the apartment on her behalf. However, once the eviction process is complete, then neither your sister nor you could enter her apartment. At that time, entering (even with a key) will be trespassing, since she will no longer have (or be able to give) the right to enter the space.