The strongest glue for plastic is JB Weld PlasticWeld, according to Craftech Industries. Craftech tested the glue on Teflon, nylon, polypropylene, TPU and PVC and only found problems when using it to bond Teflon with itself.
Other glues that Craftech found worked well were All-Purpose Amazing Goop and Loctite Super Glue (Ultra Gel Control). It found that all-purpose hot melt glue sticks were hit or miss, as some were easily broken apart after bonding over a 24-hour period. Craftech also discovered that the absolute worst glue was Testor's Plastic Cement, which failed to hold the pieces of plastic together during testing.