L&S mentions that abhinc can be used with either accusative or ablative. But no use guidance is given for posthinc. Can I use both accusative and ablative to express the length of time, or only one? The Vergilius quotes given in L&S do not express any period of time, but I would like to know how to say things like "I will go to Rome four days from now". Is it even possible to express the period of time with posthinc, or should I be using some other word? I prefer to use posthinc if possible.
As a first note, I have been unable to find a classical work where posthinc is treated as one word. The two Vergil citations in the L&S entry you mentioned actually have post hinc:
post hinc digressus iubeo frondentia capris
arbuta sufficere et fluuios praebere recentis, (V. G 3:300-301)
post hinc ad nauis graditur sociosque reuisit. (V. A 8:546)
These really are not terribly good examples of a new grammatical form. In fact, two authorities contest this:
Servius Honoratus, in his commentary to 8:546, sees it as a pleonasm. Evidently he was struck by the form enough that he even recalls the passage from the Georgics when considering the one from the Aeneid.
post hinc ad naves graditvr: unum vacat, aut 'post', aut 'hinc', ut "post hinc digrediens iubeo frondentia capris arbuta": tale est et illud "primus ibi ante omnes".
August Engelbrecht, in his Untersuchungen über die sprache des Claudianus Mamertus, pg. 102-103, sees them as two adverbs with separate functions:
Das Lexikon von Forcellini bringt auch noch in seiner neuen Ausgabe zwar zwei Stellen für posthinc bei, die jedoch beide unbrauchbar sind.... Augenscheinlich ist an beiden Stellen hinc nicht mit post sondern mit graditur (digressus) zu verbinden ebenso ist Sid carm VII 435.
Indeed, Forcellini's lexicon also furnishes in its new edition two locations for posthinc. However, neither is applicable. Evidently, in both locations hinc should not be construed with post but rather with graditur/digressus, just as in Sidonius, Carmina 7:435.
However, Engelbrecht goes on to cite a passage from Servius (caveat: although I looked where he said it was, I could not find the relevant quote) that may lend credence to the one word/form theory:
Uebrigens kann die Bemerkung des Servius zur letzteren Stelle aus Vergil, "Sunt qui posthinc unica uoce scribunt, sed perperam," als Beweis dienen dass zu des Grammatikers Zeiten posthinc = postea in Gebrauch gewesen sein muss.
Incidentally, Servius's remark on this last citation from Vergil, "There are some who write posthinc as one word, but this is incorrect," can serve as evidence that posthinc = postea must have been in use at the time the grammatician was writing.
There are examples where the hinc cannot be linked with another verb in the sentence. Here is one example from Marcus Manilius, Astronomica:
Fortunae sors prima data est....
post hinc militiae locus est, qua quidquid in armis
quodque peregrinas inter versantibus urbes
accidere assuevit titulo comprenditur uno. (3: 96-104)
Here, the only possible rendering of post hinc is a single logical "afterwards," like postea. I think that Honoratus's comment about this being pleonastic is probably applicable here. It is telling that all these examples (as well as another I found from Lucretius) occur in verse, where metrical constraints allow more creative constructions.
As for your practical question about translating, "I will go to Rome four days from now," I think in light of the above that posthinc together would not be appropriate. I recommend either the obvious post (prep) + accusative or post (adv) + ablative:
Romam post tres dies (tribus post diebus) ibo.
Or, if you would like to emphasize the "from now" part, you could certainly use hinc, in the model of Varro, De Lingua Latina, 5:144,
hinc post triginta annos oppidum alterum conditur, Alba.
Hinc post tres dies Romam ibo.
Of course it would be very difficult to find a context where hinc couldn't also be taken as a spatial adverb.