"_oku w £ajskoch"
Yes, Zazulka was right here.
So your grandmother was born in the village of £ajski, in 1896. Today this a small village, population 1300, 16 km north of downtown Warsaw, in a fork of Vistula and Narew rivers, 7 km from Zegrze Reservoir - popular tourist attraction during summer days. The surrounding areas are well forested.
After the Third Partition of Poland, in 1795, Warsaw and the Narew-Vistula forks have become a part of Kingdom of Prussia. Later this region has formally become a part of Kingdom of Poland, in personal union with Russian Empire, 1815-1916. Practically, it was under the control of Russians. Some historians called it the Fourth Poland's Partition.
Accordingly, the population of Warsaw and surrounding areas was a curious mixture. At the time when your grandmother was born the entire Polish territory was inhabited by Poles(72%), Russians(2.8%), Germans(4.3%), Jews(13.5%), Ukrainians(3.5%), Lithuanians(3.2%), Belarusians(0.3%). I guess the percentage of Russians, Germans and Jews was even higher in Warsaw and its neighbourhood.
But if you are on a quest for your grandmother's Jewish roots (I gathered that much from some hints you have given), I must disappoint you: £ajski has never been a Jewish Shtetl, although some Jewish families lived outside Warsaw, in the neighbourhood of Legionowo. There is an old Jewish cemetery in Legionowo, but again - there are probably more Russian and German cemeteries around than the Jewish ones. But there is a museum of Jewish History in Warsaw, where you can learn more details.
You will have more luck, 170 km away southwest, in vicinity of £ódź and Pabianice - where I assume your grandmother has moved later on.
£ódź was well known for its huge Jewish population, and part of £ask (which you and I had mentioned before) was a Jewish Shtetl - with general population of 4890 and Jewish population 2862 (year 1921 census) . Today's £ask is a town of 18000.