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Today I told my friend that yesterday I had read the book which my father had given me two weeks ago

Today (when I told my friend) is 23rd March; I read the book on 22nd March, and my father gave it to me on 8th March.

Did I use the right tenses in the first (that yesterday I had read the book) and the second (which my father had given me two weeks ago) subordinate clauses? Are there any alternative versions in regard to the use of tenses in these subordinate clauses?

A common trouble with ESL students is using the past perfect to talk about something in the past when sequence of events in the past is not important. The past perfect is used to talk about order of events in the past based on a reference point in the past, and is most commonly used by police, detectives, lawyers, and others who need to know the order of past events. Is it wrong to use the past perfect as you did in your example? No, but it does cause some confusion, as a native speaker might wonder why events were being ordered when the logic of the statement didn't require that. For example, if someone asked you, "What did you do yesterday?" and you answered, "I had gone to work," grammatically-speaking it is not incorrect, but it is using the near present as a reference point which is not natural.

That said, in your example, you used two markers, "today," and "yesterday" which anchor the sentence in time. The sequence of events is then, 1) Today 2) Told my friend 3) Yesterday 4) Read the book 5) My father gave it to me before yesterday. Because you used the marker "yesterday" it is not necessary to say "had" because "yesterday" as a new reference only requires the simple past.

Often for questions about tenses, a better question to ask is "Does this make sense?" For example, the statement "Yesterday, I will die," is not grammatically incorrect, but logically it doesn't make sense.

Without the time reference "yesterday", a person seeing the first statement below would infer the reading happened sometime between March 8 and March 22 (the dates mentioned by the OP)

1. Today I told my friend that I had read the book which my father had given me two weeks previously.




2. Today I told my friend that yesterday I had read the book which my father had given me two weeks ago.

Both are grammatically correct statements using reported speech.

In the second version, the reading of the book occurred before "yesterday" and the speaker's father loaned or gifted the book prior to it being read.

I see no compelling reason, other than of style, as to why the OP should change the Past Perfect tense to the Simple Past as suggested in the comments but, personally, I would prefer to keep the PP in the relative clause that begins with "which".

• 
  Me: “Yesterday I read the book my father gave me two weeks ago”
  Alice: “Was it any good?”

[That same day]

• Today I told my friend that yesterday I read the book which my father had given two weeks ago.

As an ESL learner, he or she often makes a sentence either truncated or redundant. I think an ESL should’t try to incorporate “wanted words” in a sentence. It hurts your brain and it never works that way. Here is what I can say

“I told my friend I had read the book which I got from my father two weeks ago.”