Should the table of contents of a thesis include beyond heading level 3?
I would like to know if there is a rule specifying this issue either in MLA or APA?
In general, tables of content shouldn't span more than two pages, otherwise they lose their utility of being a quick guide to the structure of the content.
A good keyword index at the rear of the document can handle many of the issues in their stead. That is, if you want people to be able to quickly see where you described the laser engraving process, then "laser engraving" can have a keyword in the index. Or if you make an argument against Talcott Parson's sick role, similarly you can note both "Talcott Parsons" and "sick role" at the back.
(note: I do encourage my grad students to CREATE extremely detailed tables of contents that lay out their entire argument. This helps them write their dissertations as it gives a roadmap and structure. But when it comes time to submit their thesis to the university, or revise for publication, they should strip their table of contents back down to a minimum of one or two levels).
A ToC (Table of Contents) serves two purposes:
In order to be efficient, your ToC must thus delivers enough information (one hierarchical level might not be enough if you have three chapters only), but not too much (hence the "two-pages limit" RoboKaren refers to). In the , the ToC is not very useful; in the other, readers are overwhelmed with information and thus perceive even less of the intended message.
It is based on these rules that you should define how much is enough. My advice would be to even strive for a one-page long ToC, with a clear contrast between hierarchical levels (I'd say indenting is not enough). I would also suggest you to use only two hierarchical levels.
Calling the first hierarchical level "Chapter" and the second "Section", here is the "official" answer from the "Chicago Manual of Style" (§1.37 in the 16th ed.):
[Sections] are usually omitted from the table of contents, but if they provide valuable signposts for readers, they may be included.
Note that in some cases, chapters are clustered into parts - where chapter numbering is not reset after a new part. In this case, parts are not a hierarchical level strictly speaking; and ToC would thus be divided in Parts/Chapter/Sections.
TL;DR: Two hierarchical levels in the ToC. If necessary (long thesis), you can include "sub-ToC" at the beginning of each chapter (again, with two hierarchical levels). Parts doesn't count.