Word 2007 does provide support for reading and producing ODF 1.1 .odt documents. You should make sure that the version of Office 2007 is current to at least SP2.
The support for ODF 1.1 is also present in Microsoft Office 2010. In Microsoft Office 2013, there is support for ODF 1.2, including interchange of OpenFormula between Excel and OpenDocument Spreadsheet (.ods) files.
The conversions implemented by products that support one native format (OOXML or ODF) are not entirely unblemished when reading/writing the other format (ODF or OOXML). You should be careful to ensure that the specific types of documents you are interested transfer back and forth without fidelity loss.
One useful aid is the Microsoft SkyDrive free service with its Web Applications for Microsoft Office. SkyDrive WebApps provide import and export of ODF as well as OOXML among the reduced functionality that it supports. If your documents go between formats successfully there, I'd say that's a safe bet. SkyDrive Web Site