What are the allowed tags inside a <li>?
Yup, pretty much. You can have lists inside lists (either inside the the inner list must be inside an <li> or just loose inside the <ol>/<ul><li>), block elements and inline elements.
To me it wouldn't make much sense to put a <table> inside an <li>, but even that's still valid.
You can use the W3C's Markup Validation Service to test against your cases to know whether or not your markup is valid.
This validator checks the markup validity of Web documents in HTML, XHTML, SMIL, MathML, etc.
TL;DR: an <li> can contain any element that is valid in <body>.
In the HTML 4.01 spec for lists you’ll find the relevant extract of the DTD:
<!ELEMENT LI - O (%flow;)* -- list item -->
This specifies that an <li> may contain flow content, which is the collection of all block and inline elements.
The HTML5 spec for an <li> is the same in that it also allows any flow content.
It's a block level element so pretty much anything goes. Trouble only comes when you're putting block level elements inside inline ones.