salesforce rest api INVALID_SESSION_ID error

How are you passing the sessionId to the /services/data/v20.0 request?, if your access_token is abc123 then you need a http header of Authorization: OAuth abc123 in the request.

API session in salesforce expires regardless if there are activities or not. to set the duration of each session go to Setup > Administration Setup > Security Controls > Session Settings>

the max is 8hours.