Any application to scan non-standard QR codes
NeoReader should match your specification:


  
  Scans all standard 1D and 2D code types – QR, Data Matrix, Aztec, EAN, UPC, Code 39, Code 128, PDF 417 and more!
  Automatic detection of code type
  


(emphasis mine)

As GiantTree identified one of your non-standard codes as "Aztec", this app sounds promising. It doesn't explicitly mention your other candidate, but that could be covered by "and more" (or we simply were not able to connect it with one of the other names).

I've personally never used this app, as I only need EAN (1D) and standard QR codes – so I can give no personal experience here. But again, rating (4.2) and votes (>30,000) speak for it. If you want to check some alternatives, be welcome to take a look at my list of Barcode Readers.