While I do not have the EF-S 18-135 IS STM lens, I will say that is a good workhorse lens for shooting everything from wide to short telephoto. You can use that lens for everything from family events, festivals, parades, flower shooting--you name it. It is a walk-around lens. Versatility and affordability are the strong points for the EF-S 18-135mm lens.
The Canon EF 70-200mm f4 L IS is a high-end telephoto lens. It is one of the sharpest telephoto lenses you can get, producing excellent image quality and brilliant colors. It is also an expensive lens, going for around $700-$1,000 on Amazon. It doesn't have the reach for shooting birds. For shooting birds, you will need a telephoto in the 300mm - 400mm range.
I'd say get the EF-S 18-135mm lens for the family shooting, workhorse stuff. For birds and wildlife shooting, look at the Canon 70-300mm L or the 100-400mm lenses in either Canon or Sigma. You will have enough of a zoom overlap for coverage between both lenses. Then for a third lens, I'd go for an ultra-wide in the Canon EF-S 10-18mm lens. You can find some excellent used copies for all three lenses, if you are on a budget.