Sustainable soil stabilization refers to using environmentally friendly and long-lasting techniques to improve the strength and durability of the problematic soil, e.g., expansive soil. Using non-energy-intensive materials with lower carbon emissions and recycled materials or waste products in soil stabilization processes can contribute to a long-term sustainable solution. The present study investigates the use of medical waste incineration ash, coal-based fly ash, and polyethylene terephthalate (PET) strips to improve the properties of the expansive soil. A comprehensive and systematic laboratory testing scheme was followed to explore the suitability of these materials. Geopolymers (0%, 5%, 10%, 15%, and 20%) are applied progressively for soil stabilization, along with reinforcements by PET strips (0%, 1%, 1.5%, and 2%). Strength improvements of the stabilized soil samples are evaluated by unconfined compressive strength (UCS), flexural strength, and California bearing ratio (CBR) tests. One-day-soaked UCS and 12-cycle wetting-drying tests are conducted to evaluate the short- and long-term durability of the samples. A toxicity-characteristic leaching procedure (TCLP) is followed to evaluate the leachate quality. The UCS, flexural strength, CBR values, and retained UCS increase with the increase in geopolymer content (GPC) and PET. The highest CBR value of 145% was obtained for 15% GPC with a 1.5% PET-stabilized soil sample, whereas the CBR value of the natural soil is only 3%. Although insignificant swelling was observed at 5% GPC, no swelling was observed for higher GPC contents, indicating reduced or no expansion for the stabilized soil. Also, after the TCLP test, the heavy metal concentration of the stabilized soil samples was detected to be within the land disposal limits for hazardous wastes, and some of the heavy metals were removed after stabilization with 20% geopolymer.