"str" is legit in generic Slavic ("*strel-", arrow), so I wonder if Polish has it, maybe in leanwords. A small dictionary computer search gave nothing. (Frankly, I just want to see a "szczrz" in print...OK, I'm German, we still can easily top that :-)
You can check the frequency distribution and see the most frequent word is strona, followed by strata and derivatives of strach. All perfectly legit.
Although, -r- in Polish is not syllabic, unlike in e.g. Czech or Slovak, which (phonotactically) somewhat diminishes the possibilities. Compare the pronunciation (stress) of Polish trwa (one syllable) with Slovak trvá (two syllables).