How can I store an array of strings in a Django model?

You can use some serialization mechanism like JSON. There’s a snippet with field definition that could be of some use to you:

http://djangosnippets.org/snippets/1478/ (take a look at the code in the last comment)

With such field you can seamlessly put strings into a list and assign them to such field. The field abstraction will do the rest. The same with reading.