Doesn't this seem odd to anyone that a virus can do this?
If by "odd" you mean "not what was expected" then yeah, lots of people. That's why they study them and the result is knowledge of things called retroviruses as WK mentioned. Incidentally, that knowledge is vital to things like finding a treatment for HIV, which is a retrovirus.
Influenza is not one. Otherwise we would have one hell of a larger problem than simply worrying about seasonal 'flu': retroviruses are not the easiest thing to treat, as the prevalence of AIDS has demonstrated, because of the very nature of the virus (being protected by basically "hiding"in our own DNA).