While expensive, many universities have site licenses that allow students and faculty to install the software for free on their devices. There is also a 30-day free trial available for those who wish to test the software before making a purchase commitment, and this is the only legitimate way to use the software for free.
The legal restrictions explain why a genuine "portable" version is unavailable. NVivo's licensing model is designed to prevent the exact use case that portable software enables. nvivo 10 software portable