Why are prepositions out of place with many phrasal verbs?
Solution 1:
There are relevant sections in 'Multi-Word Verbs in Early Modern English: A Corpus-Based Study' by Claudia Claridge, précised at http://linguistlist.org/issues/12/12-698.html which contains:
Chapter 5 examines the history of these types of multi-word verbs from Old English through to Modern English. ...Chapters 6 and 7 describe the particular multi- word verbs found in the Lampeter corpus, and attempt to describe the patterns found among them. Chapter 6 treats the data synchronically, while chapter 7 looks at diachronic developments during the 100 year period covered by the corpus.
I've accessed various portions online, but had to order a copy via my local central library.
In an article by Catherine Browman at http://web.haskins.yale.edu/Reprints/HL0594.pdf , it is stated that the transformational grammarians Absalom (1973), Chomsky (1957) and Fillmore (1965) considered the contiguous form to be basic and the separated form a movement-transformation derivative, whilst Edmonds (1972) believed it was the other way round. Other grammarians, such as Gazdar, Klein, Pullum and Sag (1985) retain the verb and particle as separate constituents, but seem neutral with regard to direction of transformation (if any).
(Still other grammarians regard the verb-particle combination as more or less unanalysable, in any given example.)
Solution 2:
These are often called "phrasal verbs" or "particle verbs" in the linguistic literature. They're found throughout the history of English, e.g. Hi ðærrihte ut eodon "They immediately out went", from Ælfric's 10th-century Catholic Homilies. However, many of the modern phrasal verbs only appear later, during the Middle English period and beyond.
Since the phenomenon is so old, it's difficult to know exactly how particles like (o)ut etc. arose. It's usually said that they develop from "preverbs", a category found in all the Indo-European languages. Preverbs (as their name suggests) precede the verb, as in the Old English example I gave above. In the history of English, the particles go from preceding the verb to following it, which is probably related to a more general change from object-verb to verb-object order.
For a fuller answer to your question, you could look at Thim (2012) or Hiltunen (1983), if you have access to them via a library. There's also a bibliography here.