Is there a word or expression for someone who uses a lot of opinions to judge himself and/or things around him (such as other people) (e.g. to "defend" himself from receiving judgement), however who is easily offended by someone else based on trivial things they say?
I don't have a single word, but an informal American expression would be
someone who can dish it out but can’t take it - someone easily criticizes other people but does not like it when other people criticize him or her
To dish out originates with the sense of serving food to people, but has taken on an idiomatic meaning of meting out severe punishment or criticism. According to Etymonline, this sense of dish dates from 1934. Taking criticism, punishment, or abuse is from the sense of take as receiving or accepting, from which the idiom taking heat also derives.
Some people would just call the person sensitive (or in jest a sensitive Sally). A common term is thin-skinned.
easily upset or offended by what other people say about you
When the person gets all upset, they could be called huffy(-puffy). When a person goes beyond huffy and gets a bit angry then we can use irascible.
Having or showing a tendency to be easily angered
I would describe such a person as pushy. Typically, people describe an overly opinionated person as pushy, but don't necessarily imply that the same person is easily offended by others' opinions. However, in my personal experience, overly opinionated, pushy, persons are easily offended by dissenting opinions. You are describing someone that always wants their way and throws a fit when they don't get it. That's pushy.