Is it possible to use the software package OpenOffice in the same way as Microsoft Office 365?

In general, the answer is "yes", but that's not really a Mathematica question.

As for import, according to the documentation (http://reference.wolfram.com/language/ref/format/ODS.html), ODS is fully supported. I don't see anything about any other specific document types. I assume that OpenOffice supports exporting to formats which Mathematica can import, so I would assume that the interoperability mechanisms would be similar. But for whatever specific import you need to do, why don't you just try it and see what happens?