Taking the radios won't be a problem. Using them in Austria is highly likely to be a problem, unless your radios operate on a radio spectrum permitted for similar use in both countries.
For example, if you are from the US or Canada, and have handheld FRS (Family Radio Service) or GMRS (General Mobile Radio Service) radios, you can't legally use these radios in Austria, as the frequencies used by these radios are already used by other services. (Austria has similar services, but they use different frequencies and you'd need to buy suitable radios locally.)
If your radios are truly Private Mobile Radio (specifically dPMR) and operate on the 446.1-446.2 MHz band, this may well be okay - you'd want to research specifically that they are permitted in Austria, but it seems they are. (You could not, however, use such radios in North America, as the 446 MHz band is reserved there for ham radio licensees only.)