I am an Indian citizen who was studying in the United States for the past 2 years. My course is completing in December 2015 and I plan to visit Germany on my way back to India, I am moving back to India permanently. My F-1 Visa is valid till 2018 but my I-20 will expire on 31st December 2015. Can I apply for a Schengen Visa from the US with an expired I-20 but a valid F-1 Visa?
Your residency status in the US is only of relevance for determining whether you can apply for a Schengen tourist visa from a consulate in the US. That you will have a change of status afterwards does not matter (at least if you tell this at the time of applying for the visa).
You can find out the rules of the respective consulate from their website. For example, in New York, you will be fine.