Applying for a Schengen visa with a valid US student visa and an expired I-20 form

Unfortunately, having an expired I-20 would make it impossible for you to apply for a tourist Schengen visa in the US. Local Schengen consulates ask for a valid I-20 in order to verify that you are a long-term resident. For example, here are the residency requirements of the French consulate in the US:

For non American citizens, a proof of resident status in the USA (green card, valid US visa and copy of valid I-20 or valid I-AP66, visas...). The visa AND the US resident status must be still valid at least 3 months after the last day of stay in the Schengen area (+ one copy of the visa, green card or relevant document). US pre-approval notices for US visas will be declined (only valid US visas affixed in your passport are accepted).

The Greek consulate has similar requirements:

For foreign students on F1 visas:

• valid I-20

• reference letter from educational institution (school/college/university) stating that you are in good standing, your major and the expected date of graduation.

You can still transit through the Schengen area if your visa satisfies the conditions of visa-free transit.