Does anyone know of an easy, effective, and preferably free way to convert Word documents with Mathtype 5.2 equations to the LaTeX format?
You may try OpenOffice or LibreOffice as an intermediary format and export to LaTeX from there. OO can handle MS Equation Editor format, not sure about Mathtype though (didn't work for me the last time I tried), maybe there are some plugins around for that.
Alternatively, if you have Mathtype installed, you can convert all equations to LaTeX in Word and then go OO -> LaTeX for the rest + some text post-processing for the equations.
Save the document as .docx and use XSLT to convert the OOXML in it to LaTeX. Free? Yes. Effective? Absolutely. Easy? Not very: it requires a detailed understanding of MathML and OOXML.