You cannot exactly insert the web parts inside that script editor of yours, but you can definitely use HTML to show the site feeds. Simple feeds in the form of rows can be used using some HTML table structures (insertRow(), etc.)
Otherwise, you can write out the entire HTML code with your Site Feed scripts and div stylings, in a different file and upload in your site, and link its path within your script editor.
(Edit) You can practically do any HTML related stuffs with your Script Editor. In this case, I’ve embedded a tag within HTML to answer your question. However, unfortunately you cannot insert List/Libraries webpart directly within it. You will have to think of some customized CSOM solutions for this
Kindly mark this as an answer if this helps you.