Should I go to engineering graduate school right after undergrad or after a few years of work experience? I've heard a few pros and cons about each. 

If you go right away, you'll just get it out of the way. 

If you wait to go, you'll learn way more and understand what's useful to focus on. 

On the other hand, if you've been earning money, it will be harder to go back to living on a graduate student wage. One professor in particular said if I thought I was going to go back to graduate school after working for a few years, I was in for a big surprise. My dad thinks the people with the best experience are those who waited to get their masters after working for a while. 

Interested in going into industry afterwards. Also considering a PhD, but have been told by the same professor that PhDs are a waste of time.
Of the opinions you heard, most make sense to me. However the most important part is what you want to do. If you are eager to go into industry and want to try that, then go with that. If you prefer to do your graduate (and maybe later a PhD), then choose that. But do not plan too far ahead, i.e.: "I'll work 2 years, go to graduate school, do my PhD, and go back to industry." Real life does normally not work like that, and if you really are trying to reach these goals they might give you more stress and worries than help you.

I, after my master degree was kind of tired of University, and worked for a company during three years. After those three years I looked into different options (for personal and professional reasons), and decided to go back in research by doing a PhD.

Try to make a list of "pros and cons", and make a decision based on that.