Is it odd to contact past graduate student? I am interested in pursuing a particular program and I find the name of some of the past students from professor's website. 
Is it odd to write an email to these past graduate students and ask about the job and their future career?
could you please tell me what should I write to be natural?
I am particularly worried about finding the job and future career.
In regards to your question what you should write I have but a few hints:

Students may be dependent for a very long time on their former advisor. Therefore, they may not want to badmouth their advisor to a stranger and answer some questions untruthfully (or ignore your request). So you should (if you want to get honest answers) formulate questions in a way such that no answer is negative. I. e. if it's very important to you that your advisor helps you a lot, you should not ask "Does the advisor helps a lot?" but rather sth. like "Is the advisor more hands-on or hands-off"? Also, of course ask as detailed as possible. The same things go for the "future career".

Since I would consider it rather impolite to start an email with many questions, you should ask by writing "Is it okay to ask you a few questions about your advisor and your future career"? Maybe you should also clarify what you mean by "future career".

If this is at all possible, you may ask to meet the students in person (of course in the way which is most comfortable to them). In a personal meeting, people are more likely to tell you true negative things (if they got a good impression of you) since their is no written trail.