Haskil was born in 1918, in Thessaloniki, to a Jewish couple, Chaym and Perla Gaegos. During the occupation of Greece by the Axis powers, the Gaegos family moved to Athens to escape arrest and deportation. There, Stella married Jacob Yehaskel.
After liberation, in 1946, Haskil started recording mostly rebetiko songs, some of which, such as "Νύχτωσε χωρίς φεγγάρι", (The Night fell moonless) and "Κάποια μάνα αναστενάζει", (A Mother is sighing), were censored due to the political climate arising from the Greek Civil War.
Among her best known songs are:
- Αράπικο Λουλούδι (Arabian flower)
- Κάποια μάνα αναστενάζει (A mother is sighing)
- Πάλιωσε το σακκάκι μου (My jacket got old)
- Ακρογυαλιές και Δειλινά (Beaches and Dusks)
- Για τα μάτια που αγαπώ (For the eyes I love)
- Γκιουλμπαχάρ (Gulbahar)
- Μπιρ Αλλάχ (Bir Allah - One God)
- Το Κατινάκι ξέχασες (You forgot little Kate)