Nothing seems to be able to read PowerPoint 95 files on a Mac. Not Office 2004, not NeoOffice (which, incidentally, completely jumbles fonts when opening PowerPoint 2003 files). The only workaround I found was to fire up Virtual PC, open the files in Office 2003 and save them in that format.
Nevertheless, even with TrueType font embedding switched on, Office 2004 failed to render the files correctly (and its metafile importing is still, er... sub-standard). So the only way to obtain a good (read-only) high-fidelity copy was to either use Virtual PC's VM Additions printer mapper (which redirects output to the Mac, and hence to a PDF file) or install CutePDF and print directly to a PDF file.
NeoOffice failed to open Word 2.0 and 6.0/95 documents correctly a number of times (it may have been tripped by character encodings or font settings, since the apparently garbled text could be copied out and pasted in new documents correctly).
Pagination was also completely garbled, although it made a valiant attempt at exporting PDFs with correct sections and headings. Replacing all non-standard font references and saving in OpenDocument format will preserve the text, but embedded metafiles and images may be garbled.
Office 2004 for the Mac seems to have no problems opening Word 95 files (except for minor formatting and TrueType font embedding issues, it wasn't tripped by them and displayed readable text). Full fidelity is, as usual, best obtained by popping the files into Office 2003 and re-saving into Office 2003 and (via CutePDF) PDF format.
However, what really saved my ass (figuratively speaking) regarding one specific document was that, in 1996, I had the forethought to save the TrueType fonts I used in a folder alongside the document - otherwise, it would have been impossible to reconstitute the original look and feel.
Neither Office 2004 nor NeoOffice seem to have significant problems with ancient Excel files (other than minor text formatting nuisances). Excel formats are a right pain to store, though, since spreadsheets are not necessarily designed for print (hence no point in doing a PDF conversion).
You're pretty much stuck without a Windows machine. Even OmniGraffle can't open binary Visio files (it can only open XML-formatted ones), and storing the files in any other format will leave you basically with a lot of lines. They might look OK, but they lack the object structure underneath.
Again, you're stuck. Fortunately there's little point in keeping these around, so I basically open them and print them to a PDF file (which entails wrestling with Project's utterly useless printing settings).