Like it or not, use it or not, every language has its dark underbelly or grammar-shunning, syntax-hating, curiously constructed, and odd sounding words that fail to get the approval of 'proper' speakers and dictionaries alike. Oddly, what we call 'slang' (slang too in Polish), is often adopted by the lingual experimental (like in the work of Polish poet Julian Tuwim and indeed many English post-modernist writers), and what was once, in times gone by, a word on the fringes, can gradually become mainstream language, with a host of associated meanings. Such is the evolution of speech.
What this does tell us is that learning a language is not just about getting your grammar right and maximising your vocabulary, it's about finding your voice and sounding like who you are. Simply put, language is one of our basest forms of expression, and in your native tongue you have your own clear way of communicating, and manner of speaking. Getting used to using colloquialisms and slang phrases is one of the central ways a language learner can quickly find and express their character. It's important to remember that both the absence and presence of slang in one's speech is telling, but understanding that it exists is crucial.
Slang in Polish is, of course, extremely prevalent. This is an old language with wide Slavic root that stretches far south to Bulgaria and the Black Sea, and East into Russia. There colloquialisms common to youth speakers, adult speakers, children, Cracowians, Warsovians, people who live in the city, people who live in the country, so on and so forth ad infinitum. Slang in Polish is varied and unmediated, just as slang should be.
There's the widely used spokόj (meaning 'cool', as in 'everything is cool', or 'cool, no problem'), favourite of the university goers and youth, the ultra-casual 'hello' style greeting, siema, and the casual 'goodbye' na ra (meaning something like, 'see you later'). There’s also a Polish equivalent of the American 'dude': koleś or ziom, or ziomek.
You can say you're really tired using skonany or wykończony, and you can let people know how great something is using one of either, kapitalny, super, genialny or rewelacyjny. The slang way to say thank you is either dzięki or dzięks, and a lot of people use the adopted English phrase sory to apologise.
A really important one in Poland, a nation famous for its drinking culture, is na zdrowie, zdrówko, both equivalents of the English 'cheers'. In Poland, to get someone to down their drink, you'll have to shout do dna (literally meaning, 'to the end').
There's Polish equivalents of calling your parents your 'old boy' and 'old girl', but these can be considered to be rude, so be careful where you use them. They are moja stara (literaly, 'my old') and mój stary (again, 'my old', but masculine).
These are just some of the examples of Polish slang, some of which are used more widely than others. Remember that understanding register is important for learners of any language, it's the way speakers know what is appropriate to say and where. It's a warning worth remembering when it comes to slang too, because in Polish, just as in English using some of these phrases in the inappropriate situation can get you in a bit of a pickle!