The root √BEL “strong” has a long history in Tolkien’s writing. Its most notable derivative is S. beleg “great, mighty”. This word dates back all the way to the Gnomish Lexicon of the 1910s, where G. beleg already had this meaning (GL/22). In this document, its Qenya equivalent was ᴱQ. velike, meaning the early root must have been ✱ᴱ√ɃELE: in Early Quenya, ancient initial ƀ- > v- but initial b- > p-.
The root ᴹ√BEL appeared in The Etymologies of the 1930s with the gloss “strong” and a number of Noldorin, Telerin and Ilkorin derivatives starting with bel- and having to do with strength (Ety/BEL). In the 1930s this root had no Quenya derivatives. The root √BEL reappeared in a list of “large & small” roots from around 1968, where it had the variant √MBEL and was also used in its extended form √MBELEK as the basis for the Quenya name Q. Melkor (PE17/115). This extended form was also given as the basis for S. beleg in these notes, which was given the glosses “large, great” implying the root had as much to do with size as strength.
This note indicates that S. beleg began with an ancient nasalized stop, but various mutations elsewhere in the corpus imply this was not the case, such as the soft mutation in S. Cûl Veleg “Bigload” (RC/536) and the nasal mutation in S. Taur-i-Melegyrn “Forest of the Great Trees” (WJ/185). I suspect the ancient strengthening of initial b- to mb- must have been limited to the Quenya branch of the language; see the √MBELEK for further discussion.
The unglossed root ᴹ√STALAG appeared in The Etymologies of the 1930s with derivatives like N. thala “stalwart, steady, firm” and N. thalion “hero, dauntless man” (Ety/STÁLAG), the latter a sobriquet of Húrin typically translated as “Steadfast” in the narratives themselves (S/199). Similar forms appeared in Early Noldorin Word-lists from the 1920s derived from the primitive form ᴱ✶stalga (PE13/153).
The root √STAL “strong” was mentioned in passing as the basis for the adjective Q. astalda in a rejected page associated with roots having to do with “large & small” words, probably from the late 1960s (PE17/115; VT47/26 note #26). The name Q. Astaldo “Valiant” appeared as a sobriquet of Tulkas in later versions of The Silmarillion (S/28), replacing the earlier name Q. Poldórëa of similar meaning (MR/146, 149; LR/206). For purposes of Neo-Eldarin, I would assume √STAL (and its derivatives) means “✱valiant” rather than “strong”.