When people talk about Old English, they typically mean Shakespeare or the King James Bible or any flowery language with "thee"s and "thou"s. Which isn't Old English at all. Elizabethan and Jacobean English are both just older forms of Modern English. The fact that modern speakers of English can read these writings without advanced degrees pretty much says it all. Sure, the older dialects had more grammatical complexity than we are familiar with (separate personal and familiar second persons, distinct conjugations for first, second, and third person singular, etc.), but overall, Modern English is a pretty simple language, grammatically.
This is in contrast to the works of Geoffrey Chaucer, such as the Canterbury Tales which is written in Middle English... which they have to release in English speaking countries translated from the original English to modern English. Here's a section of it:
Whan that aprill with his shoures soote
The droghte of march hath perced to the roote,
And bathed every veyne in swich licour
Of which vertu engendred is the flour;
Whan zephirus eek with his sweete breeth
Inspired hath in every holt and heeth
Tendre croppes, and the yonge sonne
Hath in the ram his halve cours yronne,
And smale foweles maken melodye,
That slepen al the nyght with open ye
(so priketh hem nature in hir corages);
Thanne longen folk to goon on pilgrimages,
And palmeres for to seken straunge strondes,
To ferne halwes, kowthe in sondry londes;
And specially from every shires ende
Of engelond to caunterbury they wende,
The hooly blisful martir for to seke,
That hem hath holpen whan that they were seeke.
That, above, is MIDDLE English. That isn't even Old English. Here's some Old English:
HWÆT, WE GAR-DEna in geardagum,
þeodcyninga þrym gefrunon,
hu ða æþelingas ellen fremedon!
oft Scyld Scefing sceaþena þreatum,
monegum mægþum meodosetla ofteah,
egsode eorlas, syððanærest wearð
feasceaft funden; he þæs frofre gebad,
weox under wolcnum weorðmyndum þah,
oð þæt him æghwylc ymbsittendra
ofer hronrade hyran scolde,
gomban gyldan; þæt wæs god cyning!
Ðæm eafera wæs æfter cenned
geong in geardum, þone God sende
folce to frofre; fyrenðearfe ongeat,
þe hie ær drugon aldorlease
lange hwile; him þæs Liffrea,
wuldres Wealdend woroldare forgeaf,
Beowulf wæs breme --- blæd wide sprang---
Scyldes eafera Scedelandum in.
Swa sceal geong guma gode gewyrcean,
fromum feohgiftumon fæder bearme,
Notice it still even uses runic characters, such as Þ and ð. There's a "wide sprang" in there, and I can see some "he"s and "him"s, and I can make out an "oft".
So now that we're clear what Old English is, some neat facts. It had grammatical gender, much as modern Romance languages. It also had separate nominative, accusative, genitive, dative, and instrumental cases for nouns.
In modern English, most of that complexity is gone, sadly, and readers who haven't taken Greek or Latin (or Russian) probably won't know what it means for a language to have accusative case.
Most English speakers have at least a familiarity with Romance languages such as Spanish or French, and therefore know that in those languages, verbs require specific conjugation, changing form based on their time frame and mood and the person involved and hundreds of other things. When verbs change, it is conjugation. Which is all hard to keep up with for English speakers, where verbs are basically past tense or present tense, third person or every-other person. There's still some of this left over in verbs such as "to be", but not a lot of it.
In some languages, even nouns change, and this is called declension. And in Old English, nouns were declined.
Modern English only retains three "cases" -- subjective, objective, and possessive -- and these only in the pronouns. If you say "I", then you are the subject of a sentence. If you say "me", then you are in some way the recipient of the action of the sentence. If you say "my", then you are the owner of a thing in the sentence. The same goes for "he" "him" "his"; "she" "her" "her"; "ye/you" "you" "your"; "thou" "thee" "thy"; "who" "whom" "whose"; etc. Not even all of the pronouns have separate forms anymore for separate cases, but the most effective way to demonstrate that a character in a book or show is stupid is to have them use "me" in the subjective; i.e. "me not like". (Which is ironic that we project this on "cavemen", when ancient Proto-Indo-European had far more grammatical complexity than even Greek or Latin. They might see us as inferior simpletons for using a single case for both direct and indirect objects.)
Anyway, I've been trying to find English words that still carry case information. I remember coming across a few, but the main ones are English place pronouns. Since these are pronouns, they managed to retain case information like the personal pronouns, but because they are place and not personal, the information they carry is different from the standard subjective/objective/genitive.
Hence/Thence/Whence : Ablative. These words automatically contain "from" in their meaning. So "hence" means "from here"; there's no need to say "from hence", and it's actually kind of wrong to do so. So "take that hence", or "cast in to the fiery chasm whence it came."
Hither/Thither/Whither : Objective. These words automatically imply "to". So "go thither", or "bring that hither", or "whither are you going?". I initially thought these were accusative, but it seems dative use is also acceptable (that is, "come hither" and "bring it hither" are both correct).
Herein/Therein/Wherein : Locative. I guess these words are more or less just "in here" swapped around? They still convey case information. So, "the letter is herein" when referring to a stack of papers on my desk. At my most pretentious, I might say "bring that hence" to tell someone to take something away (not like I'd expect them to understand what it meant...), or "bring that hither" to tell someone to bring something here. But "bring that herein" just seems... wrong... even if you wanted the addressed to bring something inside the place where you were. Using "herein" or any of its cousins such as hereupon, hereby, hereunder, hereat, et al., with any objective sense (i.e. as direct or indirect objects of a sentence) doesn't seem to work. Though the letter is herein, I wouldn't ask you to place it "herein". It seems then that these words have a slightly more bare meaning of location, signifying precisely that that a thing is located somewhere. I might be wrong on this, but I have difficulty finding counterexamples. Please correct me if you can; grammar is only a hobby of mine.
Like I said, the mains ones I'm aware of are spatial pronouns.
The only other example I can think of, of noun case being present in English grammar, is that in modern colloquial English you could effectively put any noun in to the instrumental case by averbifying it. As in, "hit the nail hammerly". It sounds pretty silly, sure, like something from the good doctor Seuss, but it still conveys that you should use a hammer to hit the nail; "hammer" has been put in to instrumental case. Howabout "I arrived carrily"? Here, it is slightly more ambiguous if "carrily" is the means by which you arrived or the condition in which you arrived. So maybe it doesn't work perfectly, but it's something.
I'm still looking for more words like this. I have done a lot of internet searching, and it is absolutely impossible to find any information about this. All the references are either to Greek tutorials or simple 3rd grade grammar lessons about English subject/object/possessive distinction. Since no one else had bothered to touch it, I thought that I might.
If you know of any nouns in English that convey grammatical case besides the standard ones, then please share. I'm certain there are more, but I've forgotten them.