This is a very interesting book considered "Level 4" for people who are trying to learn the difficult English language (and is especially helpful for those transitioning from Eastern languages to Western languages). In my opinion, there are three important themes in Nothing But the Truth are truth, adventure, and friendship.
The themes of truth, adventure, and friendship are shown through the character of Hu, who goes to an international school in Bangkok. Why is one of themes truth? Because no matter what Hu does in this book, she is presented with a conundrum as to whether to tell the truth or not. Through some trial and error with both teachers and friends, Hu gets through it and learns the importance of ONLY telling the truth. As Hu learns about truth, she goes on all sorts of adventures and meets new friends (hence the other two minor themes). One of her adventures Hu takes is traversing a national park and also starring in a school musical. Each of these adventures also teaches Hu something about truth.
Therefore, as you can see, truth is the main theme of the novel (while adventure and friendship are minor themes). The neat thing about the book is that every single Hu-situation revolves around truth in some way.