For Japanese, the accusative case marks the direct target of the verb. Much like the dative case marker 「に」being derived from an original lative meaning, the accusative is likely derived from an earlier perlative meaning. The sense of “moving through or along” was applied to action verbs to mark the noun which the verb acts “all the way through.” This is also supported by the facts that 1) 「を」can compound with the topic particle (which sometimes results in a voiced variant 「をば」) and 2) the direct object of transitive verbs is not obligatorily marked in earlier stages of the language (which persists even in the modern language).
I have found that many sources have uses for the accusative which are not at all congruent with the basic meaning of the particle 「を」. Looking more closely at them, it is apparent that in these examples, the verb is always a verb which has some inherent sense of motion out of or away from a deictic center, which in Japanese are always transitive verbs. That is, verbs like modern 「出る」 ,「離れる」, and 「遠ざける」mark their point of separation with 「を」where most other languages with grammatical case use the ablative (“from”) if they have it.
Accusative of Place through Which (Perlative Accusative)
The accusative marks the place through, along, or past which a verb of motion is carried out. This use also applies to verbs which refer to motion through time.
あまたの御方々を過ぎさせたまひつつ － 多くの女房をお通り過ぎになっていて
千年を過ぐすとも － 千歳を過ごすとしても
宇多の松原ゆきすぐ － 宇多の松原を行く
直道を行かんとす － 近道を行こうとする
松原を経て行く － 松原を通って行く
Accusative of Direct Object
The accusative marks the direct object of transitive, volitional verbs. Note that many verbs that were once transitive have taken on other particles in Modern Japanese. As stated above, this also applies to verbs with an inherent sense of separation.
竹を取りつつ － 竹を採取しつづけて
あの国の人をえ戦はぬなり － あの国の人ととても戦えないことだ
かぐや姫のやもめなるを嘆かしければ － かぐや姫が寡婦（やもめ）になったことが嘆かわしいので
都を遠ざからんも － 都を遠ざけようも
Sometimes, 「を」marks a direct object which is semantically similar to the verb itself; this is used for emphatic purposes.
昼は日一日（ひとひ）寝（い）をのみ寝（ね）暮らし － 昼は一日中寝ることをするだけで日を暮らし
「の」can be found designating a direct object in Genji Monogatari. It seems that in these cases, the clause in which it is used is subordinate, mirroring the alteration of 「が」 and 「の」 when marking the subject in similar clauses. It is also possible that in these cases, the construction is similar to the modern 「～がする」constructions.
珍しき様のしたれば － 珍しい様子をしたので
From the Kamakura Period onwards, it is common to see 「の」marking the direct object. This is actually the result of a final moraic /n/ occurring before particle 「を」. The process is such: /n/ + /wo/ > /nno/ (んの）. This reflex can be seen in Portuguese accounts of late Middle Japanese: 仙翁花（せんをうけ）is transliterated as Xennoqe [ɕen.nō.ke].
油断のさせまいことぢゃ ＝ 油断をさせまいことぢゃ