The best way to find a cheap fare is to book your ticket as far in advance as you can and to avoid traveling at rush hour.
This is the last train of the day.
Find all the dates and times for this journey
3 h 33 m
4 h 37 m
Trains per day
It's difficult to get from Strasbourg to Duisburg without changing at least once.
Here are some other resources that might have the information you need