There is a small bed, a fan, a table and many books in my room.

There are many books, a small bed, a fan and a table in my room.

It depends on the first thing following the verb; not the entire sentence.

"There is a small bed, a fan, a table and many books in my room."

If written out fully, it would read  '"There is a small bed, there is a fan, there is a table and there are many books in my room."

Only the first 'there is' is used ;  however, if you were to put the books first, it would read  'There are many books, a small bed, a fan and a table in my room'.