I have several domain names on different domain registrars (as Godaddy, Namecheap, Name.com) and on my hosting control panel, I am putting them as addon domains for another domains. Would the addon domains really affect Google position my main sites in search engine results?
No they doesn't effect website SEO. Just make sure to optimize them properly to help rank them higher in Google searches.
Nope, this is just a feature with your web hosting companies control panel, it has no effect/effects on SEO. A addon domain is another domain name you attach to your webhosting account, allowing you to host 2 websites within the same hosting account. As long as you don't have the exact same website on both domains. You'll be fine, you shouldn't inter-link websites on the same host, as they'll all be on the same IP.
Add on domains do not have effect on SEO as well as your website ranking at all.