Some English dialects can be said to have inverted word order, unclear pronouns, and nonstandard, or variable, spellings, but your question goes beyond this in asking whether this is true of the Elizabethan English of Shakespeare, the Middle English of Chaucer, or the Old English of such as “Cynewulf and Cyneheard.”
While Shakespeare and other Elizabethan writers may on occasion invert word order to make a point by using the rhetorical and literary device hyperbaton, which has subcategories anastrophe, hysteron-proteron, and hypallage, Elizabethan English honored the same SVO (Subject Verb Object) order that governs English today, as in this line from Shakespeare's Troilus and Cressida: "Call here my varlet; I'll unarm again" (1.1.1). However, spelling in the Elizabethan era had not become standardized, so spellings had variability, though pronouns were clear in their designations.
Middle English, the English first introduced into literary writing by Chaucer, also generally follows the current SVO order as in seen in this quote from Book of the Duchesse:
1 I have gret wonder, be this lighte,
2 How that I live, for day ne nighte
3 I may nat slepe wel nigh noght,
4 I have so many an ydel thoght
You can see that aside from the presence of extra adverbs and negators (e.g., that in "how that I live"; nat and noght in "nat slepe wel nigh noght"), the clauses follow the SVO order ("I have gret wonder"; "I have ... ydel thoght"). Spelling was even more variable in Middle English (ME) than in Elizabethan English. Pronouns in ME were less dependable than for Elizabethans. For instance, the current simple pronouns her and him weren't so simple in ME, for example:
her or hir: their, them, or the plural of he
hir: her; to her; of them; their
Old English employs several various sentence orders. As explained by Murray McGillivray Ph.D., Old English may vary the current Subject (S) Verb (V) Object (O) order with VSO, VOS, or OSV, as well as follow the SVO order. Borrowing from McGillivray, this OE sentence (with its Modern English translation beneath) is written in OSV order:
OE: ær hine (O) þa men (S) onfunden (V) þe mid þam kyninge wærun
ModE: before the men (S) discovered (V) him (O) who were with the king
Spellings were variable and OE pronouns, earlier forms of those in ME, had some differences within the variability:
he: he, him
Therefore, when comparing these three types of English, Old English is the one that has intrinsic inversion of word order (as opposed to word order inverted for literary and rhetorical effect), variable spelling, and unclear pronouns, though there is some overlap into Elizabethan and Middle English in the second and third categories.