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As Japanese is a subject-object-verb order language, and English is subject-verb-object, most analysis of word order between the languages only emphasises the differences between them.

However, let's have a look at a particularly complication example.
Imagine, if you will, a young boy, who has some homework to be getting on with. He'd rather be playing with his friends, but his dad makes him get on with it.
On the way to school the next day, he relates this to a friend.
'I didn't want to be made to do homework by my dad'

How could we say that in Japanese?
僕はお父さんに宿題をさせられたくなかった。

That's a very long verb at the end there, so we can break it down into units of meaning.

お父さんに by my dad
宿題を homework (object)
させ made to do
られ (passive) to be
たく want
な not
かった (past tense) did
（僕は) I

Reading from the bottom, the word order is exactly reversed.
You may think that splitting a word up in that way is strange, but although word order in Japanese is relatively flexible, the constituent parts of a word have a fixed order. Why have these constructions become fixed, and why in reverse order from English?

Unfortunately I haven't got any answers, but these patterns hidden within languages go to show how similarly human beings think.

Reference
日本語の教科書 畠山 雄二

Regular vowel movements

Previously, I mentioned how there is a pattern in the way numbers are formed in Japanese, with only changes in vowels between related numbers. However, although it is unusual to find such a relation in numbers, the phenomenon is very common in natural languages.

Just to recap, one hito and two huta, share a common root in h_t_. Three and six are both m_, and four and eight are both y_. Change the vowel to double the number. In modern Japanese such vowel changes are rare, but their former importance in the language is still very clearly evident.

Transitive verbs and intransitive verbs often show this relation, although there is no regular pattern for all verbs. I'll talk about these in more detail another time.
あげる　ageru (to raise) : あがる agaru (to rise)
しめる　shimeru (to close something) : しまる shimaru (to close by itself)

There are some common nouns that change in a few compounds. Many of the compounds have been absorbed to the point that they are considered as words in their own right.

• 瞼 mabuta = 目 me + 蓋 futa
• 手綱 tazuna = 手 te + 綱 tsuna
• 杯 sakazuki = 酒 sake + つき tsuki
• 風見鶏　kazamidori = 風 kaze + 見 mi + 鶏 tori
• 爪楊枝 tsumayōji = 爪 tsume + 楊枝 yōji
• 木陰 kokage = 木 ki + 陰 kage
• 炎 honoo = 火 hi + の + 穂 ho

These seem quite random at first, but closer inspection reveals two groups.
A final e mutates into an a, and a final i mutates into an o.

me ⇒ ma
te ⇒ ta
sake ⇒ saka
kaze ⇒ kaza
tsume ⇒ tsuma

hi ⇒ ho
ki ⇒ ko

Clearly it isn't a random change, but it's far from universal. 毛 ke never forms compounds as ka*, 血 chi never mutates to to, and 竹 take is never taka. The rule that determined how vowels alter in compounds is dead, but its spirit lives on in daily vocabulary.

Once the change has become established, it is then only a small step for the modified form to take on a new meaning. For example 魚, now normally read as さかな. The common reading used to be うお, and さかな was written 酒菜 (sake + vegetables) meaning something eaten with sake. Now the original meaning has been lost completely, a process which was made all the easier by the change in the vowel.

By way of comparison, Proto-Indoeuropean, the language from which most European languages originated, modified words through vowel mutation, and relics of this system are still found in English as so-called irregular plurals and verbs.

So, for plurals:
mouse ⇒　mice (both have the form m_s)
foot ⇒ feet (both have the form f_t)

and verb tenses:
sing ⇒ sang ⇒ sung (a common s_ng root)

Also, there are related words that come from a common source: sit, seat, set. All have the common s_t root.

Now the pattern in the Japanese numbers doesn't seem quite so strange. In both modern English and modern Japanese, new words are usually made by adding a suffix or prefix. The lack of living examples of vowel mutation means that it is not obvious how the process took place, so we shove the words that have resisted the new rules into a category we call 'irregular', forgetting that these were once the regular forms.

In the same way, the rule that determined the significance of the vowel changes in the numbers 1-10 died hundreds, possibly thousands of years ago, but its been passed on through the generations as a hidden message from ancient history.