.docx is actually an XML-based format, and is more "open" than the old proprietary
.doc format was. However, the XML processing logic inside Microsoft Word is still closed-source, and while LibreOffice (and others) may try and emulate it as best they can, there likely still will be some differences in rendering between the two programs.
.odt is also XML-based, and I quickly found this plugin that lets you read them in MS Word, although you may run into the same formatting/display issues you're seeing now going in the other direction.
If you truly want formatting to stay as close to the original as possible, safe your documents as PDF files. That is a standard that everyone understands, especially when it comes to image placement. Different programs have varying abilities to edit PDF files that have already been created (I sprang for Acrobat 11, and I love it), but if you're just going for consistent presentation then PDF is the way to go.