where- and there- compounds

Solution 1:

They both mean the same thing and I don't think are archaic. The first is a good choice for day to day standard, business or informal English. While the second is more appropriate in formal settings. So if I am writing a legal document, I'd use the second, otherwise, I'd go with the first one. But that's just a matter of style and you will not raise an eyebrow if you switch them around.

Solution 2:

In colloquial speech, one is most likely to hear 'the book I read that in', but this sounds ugly to me.

One will hear 'the book in which I read that' occasionally in colloquial speech, but mostly in formal contexts.

'The book wherein I read that' is most frequently used in legal contexts, but even there it is probably less common than the other two.

You may receive odd looks for using such compounds in colloquial speech, but there is nothing wrong with them. They do, however, retain an archaic flavour. My recommendation is to use them conservatively and to be mindful of your audience. There are a few idioms in which such compounds can be used without a second thought, such as 'a lack thereof' or 'therein lies the problem'. 'Therefore', 'hitherto', 'henceforth', and 'heretofore' are some such compounds that have survived the years.