To answer your question: Yes, as far as I know there is ONE practical application for Venn diagrams (BTW I seem to be older than you because I first was introduced to "Euler" diagrams and then learned that Venn diagrams were the same): The so-called KV (Karnaugh-Veitch, not sure about the spelling) diagrams. They can be used to convert - uhm - truth tables (?) into boolean expressions.
Since I neither know whether you are familiar with boolean algebra nor am sure about my english terminology let me give you an example:
Should you marry her? You have three inputs:
A: She is pretty. (1=yes, 0=no)
B: She is rich. (1=yes, 0=no)
C: You love her. (1=yes, 0=no)
You want to obtain one output:
D: You should marry her. (1=yes, 0=no)
Now you write down all possible input combinations as a table and assign an output to them at your will, for example:
If you are familiar with KV diagrams you can convert this to the boolean equation
D = (A and B) or C
In human words: You should marry her if she is pretty AND rich OR if you love her.
The boolean form is for example needed when you want to make an electronic circuit that gives you this advice or when you want to program the logical decision. The example I chose was once sold as a demo construction set for logical gates ("marriage indicator").