If you are looking to host feature like stackoverflow on your own website then it would definitly upset you coz open source version of stackoverflow is not available.

Stack Overflow is a question and answer site for professional and enthusiast programmers. It is a privately held website, the flagship site of the Stack Exchange Network, created in 2008 by Jeff Atwood and Joel Spolsky.

Stack Exchange has released an updated, feature-complete version of the Stack Overflow engine which is now available for enterprise use. You can compare the feature out here.
https://stackoverflow.com/teams/pricing

So What are the best alternatives to Stack Overflow which you can host on your website and similar to Stack Overflow? Here are some of the those as follows:

• Dev.to – Ruby – https://github.com/thepracticaldev/dev.to
• question2answer – http://www.question2answer.org/
• ASKBOT: Python/Django. Hosting, code, docs, import. GPLv3
• Biostars: Demo. Python, Django. MIT license
• Django-knowledge: Demo. (July 10, 2019: Repo is read-only) Python, Django. ISC license
• LampCMS: Demo (June 13, 2019: Demo sites do not work). PHP 5.3, MongoDB. LGPL3
• Mamute: Demo 1, Demo 2 (June 11, 2017: Demo sites do not work). Java. Customizable. Apache 2 license
• PaizaQA: Demo, MEAN (MongoDB, Express, AngularJS, and Node.js), MIT license
• Kliqqi: PHP, MySQL. Different look, hosting. Not active, CC-BY 3.0 license
• Question2Answer: Demo. PHP, MySQL. Fairly active. GPLv2+
• Scoold: Demo, Java, active since Jan. 2017, Apache 2 license
• Talkyard: Demo. React.js, Scala. Also has open-ended discussions & chat. Hosting, code, installation. AGPL.
• Vanilla Forums: Demo. PHP, MySQL. Forums with Q&A config option. Active and has Commercial and Open Source plans. GPLv2