Learn English – Is it correct to say “I wished I had learnt something somehow”

The had have construction in an if-clause is an example of what is commonly called the double perfect. This extract from grammar.about.com cites The Cambridge Grammar of the English Language's discussion of the usage, which it calls non-standard:

"Instead of an ordinary preterite perfect, a non-standard 'double perfect' is often found:

(9i) If it had've come yesterday he would surely have told her.
(9ii) I wish he hadn't've left.

This is largely restricted to speech (or the written representation of speech). It appears to be increasing in frequency, and though it is not as yet established as a standard form, it is used by many who in general speak standard English. From a grammatical point of view, it is a curious construction in that had is followed by a plain form, not a past participle; it is normally reduced to /əv/, and in writing is sometimes spelled of, indicating that it is not perceived as a form of have."

(Rodney Huddleston and Geoffrey K. Pullum, The Cambridge Grammar of the English Language, Cambridge University Press, 2002)

There's an extended discussion of the issue in Counterfactuality in non-standard subjunctive conditionals. The authors claim that there is a semantic difference between the standard and non-standard forms. Here is their opening section which offers references to possible explanations for the 'extra piece of morphology'.

1. On standard and non-standard subjunctive conditionals: The data

English subjunctive conditionals can adopt different forms. The standard form of subjunctive conditionals (SC) is illustrated in (1). However, speakers of some dialects of English also accept some of the variants in (2) as subjunctive conditionals. The forms in (2) differ from (1) in that they include: would or had.

(1) If Jones had taken arsenic, he would have shown some symptoms. [SC]

(2) If Jones would have/ had have/ would’ve/ had’ve/ woulda’/ hada’/ would of / had of taken arsenic, he would have shown some symptoms. [NSSC]

The non-standard forms (NSSC) exemplified in (2) appeared in the 15th C, at the time when the subjunctive voice in English disappeared (Huddleston & Pullum 2002). While the NSSCs mark different registers, no differences have been observed in terms of interpretation between an NSSC and an SC. The extra piece of morphology has usually been considered vacuous: a redundant repetition (Wilson 1993), a phonological harmony effect (Molencki 2000), or a psychological effect (Boyland 1995).

The aim of this paper is two-fold: a) we present a novel empirical observation: we claim there is a contrast in meaning between (1) and (2); and b) we offer an analysis that predicts the differences in meaning.

Yep. The two hads here are serving different purposes.

The first one tells you when the thing happened, the second tells you what happened. An easy way to see this is to change the second had to a blank and then fill in that blank with some other verb, as in:

It is interesting, too, that his father had used / gone by / been given the same name

had had is a pretty common construction. That said, I'd agree it sounds weird, and I doubt your confusion about whether it's grammatical is uncommon, which is one reason I avoid it wherever possible. I've never found a situation where it couldn't be replaced with something that flowed better conversationally.