1. I have a Visio drawing with a VSDX extension which I know is 2013.

2. I downloaded the visioviewer32bit from Microsoft downloads and did the install.

3. The notes said that this should allow the web access viewing of the document but it doesn't. Irregardless of whether I try to "open" it on Office 365 (somewhere between 2013 and 2010 SharePoint) or a local SharePoint 2010.

a. if I try to view it under Office 365, I get a message asking if I want to open or save the file from kcmo.sharepoint.com. If I answer Open, I get message that Windows can't open a file. but then I cannot find a program to open it.

b. If I try to view it under our local SharePoint 2010 (which handles VDW format), the program wants to know if I want to Open, Save or Save As. I pick Open and it asks if I want to save it.

Any ideas?

Let's try to sort the things out:

1. VisioViewer and web access are more or less unrelated. Visio Viewer allows you to open files from your computer without installing Visio. After installing Visio Viewer, you should be able to open .vsdx files on your computer for viewing. Make sure you install the latest Visio Viewer 2013.

2. SharePoint 2010 cannot render Visio 2013 (.vsdx) files, only VDW files.

3. If your SharePoint 365 has Visio Services enabled (included in the subscription), then you should be able to view Visio files (both .vdw and .vsdx) online, directly in the browser, without any extra software installed on your computer.

Take a look at this post, maybe it will be helpful:

Mixing Visio versions and SharePoint versionswhat works and what does no

As for 1. after installing the viewer, I tried to open the vsdx file and it did not work.

as for our Office 365.. it does not open the vsdx file either.

I guess for now, I will try and have the drawing saved in a lower format. Thanks

That's odd. Normally Visio Viewer opens Visio files, that is it's only purpose :)
Maybe the file was somehow corrupted? I think the best could be, you ask for another copy, right.