Opening shapefiles without prj-file (one of Gauss–Krüger CS) in QGIS

You can try to reproject your whole project with the QGIS-button in the bottom-right:

or just reproject your shapefile-layer to the crs used by gmaps wms.

This done via right-click on the shape-layer -> "Properties..." -> "Source"-tab:

You got many different tools to accomplish this task.

You should find a way with the tools from processing if you search for "proj"

• If you dont have a .prj file with your shapefile then you're using Assign projection
• If you've got a .prj file then better use Reproject layer

In both cases you need to know what your needed CRS / EPSG code must be.

As DirkB already pointed out, you need to use the Assign projection tool from the Processing Toolbox. Do this for both of your shapefiles, then they should display correctly. knutella already hinted at the possibility to change your map's projection, so adjust this to fit your needs.

Aside this, I personally recommend to scratch OpenLayersPlugin and use QuickMapServices instead, with which I had fewer issues when it came to projections and printing maps. You can also enable additional providers (per default, many of the good ones are disabled) by going to:

Web --> QuickMapServices --> Settings

then click on the More Services tab and click Get contributed pack. Save, exit, have fun with it.