Here's a pic of my broken glasses:
The glasses have broken on the top corners and hence the sticks have separated as seen in the pic. Is there any way I can stick/fix the glasses? Any glue? Any hack?
You can use cyanoacrylate glue to fit the "glass" back together. The bond will probably not be as strong as the original if it is glass.
Follow the instructions on the glue bottle for the best results.
A lot of glass lens are made from some type of plastic material. Glues can damage the lens in those cases.
The only good repair is to replace the lenses.
My glue of choice for projects like this is a quick set (5 Minute) Epoxy. Since the break is not in the line of vision, the repair should not effect functionality. I'd first carefully repair the breaks one at a time, and then after it has cured for an hour or so, I'd place a reinforcement along the top and epoxy it in (anything from a metal brad to a tooth pick) would do --- cover it with a generous amount of epoxy & let it all set for several hours before using the glasses. Be careful to avoid finger prints from sticking to the glass, perhaps coating just non-glued sections with a light coat of vasoline or soap.
You can buy a cheap glasses which has the most appropriate framing for the lenses you have. And then try to place those lenses on the new frame.
After finding a cheap frame like in the picture below, you can even get your lenses re-shaped / re-formed by an expert. Maybe you can try it on your own to round the corners using sandpaper.
Most lenses are made of plastics chemically similar to acrylic or polycarbonate. That means they can be "welded" with solvent glues that work on those plastics -- Ambroid ProWeld is the brand on the bottle I have at home. Exercise extreme care, as the solvent will cause either surface distortion of frosting if it gets on the surface of the lens -- hold the lenses upside down so drips run off instead of into the field of view, and coat areas away from the joint with oil or grease to protect the surface.
Follow the instructions on the bottle -- usually, you'll dry join the pieces and apply the tiniest possible drop of solvent to the joint where it runs to the edge of the lens. Done carefully, this can produce a nearly invisible join as strong as the original, unbroken material -- and unlike other types of glue, won'tn preclude gluing with another adhesive if it doesn't work; the solvent will evaporate cleanly.