Perform fuzzy lookup to partially match the address column
This problem is called record linkage. This process usually involves comparing records using an approximate string similarity measure.
Here are a few related questions on the site that I'm aware of:

About string similarity measures, you might find some info in these questions.
About record linkage, I'm aware of these questions.

(Note that there are certainly many other questions/resources available, I just mentioned the ones I remember)