When do I need to use an OR gate IC?
You should not wire outputs together, ever (excepting open drain types or special types designed for such use). Push-pull outputs will "fight" if any one is at a different output voltage to the others, draw excessive current, and will not necessarily provide valid or correct logic levels at the output. 

In order to combine the 4 XOR gates you could use a 4-input OR gate (eg. CD4072) or a 4-input NOR gate eg. CD4002 (which would have an inverted output compared to the OR gate). 

As implied by the lower number, NOR is a more common function in 4000-series CMOS than OR, but both are still easily available.