They do all mean generally the same thing, but as always examining the difference can be revealing.
日本に来た2日後にこの本を買った is structured like (日本に来た2日後)にこの本を買った. 日本に来て2日後にこの本を買った can be parsed the same, but it can be also parsed as 日本に来て(2日後にこの本を買った). This difference becomes more visible when you remove 2日後に:
- 日本に来たこの本を買った (I bought this book that came to Japan)
- 日本に来てこの本を買った (I came to Japan and bought this book)
来てから is 来て+から and the extra から emphasizes the ordering or causal effect. The speaker really wants to communicate that the purchase of the book happened after he came to Japan, and presumably the context demands that emphasis, for example someone said the book was really popular back in the US.