Above one hundred, I'd figure (based on the greeting 'Sto lat!' not 'Sto laty!') that it's genitive followed by which ever base number number follows, e.g. One-hundred vs. One hundred-and-one houses etc..
100 - sto lat Gen
101 - sto jeden lat - Gen
102 - sto dwa lata - Nom
103- sto trzy lata - Nom
104 - sto cztery lata - Nom
105 - sto pięć lat - Gen
...
Always look at the last part of the numeral. With plural number, 2,3 and 4 are in Genitive case, all the rest take Nominative.
But note:
12- dwanaście lat - Gen
13 - trzynaście lat - Gen
14 - czternaście lat - Gen
- it's because 12, 13 and 14 are one-word numerals and not compounds.