[subject] + 受 + [verb]
[subject] + 受到 + ([agent] + 的)+ [verb]
[subject] + 很 + 受 + [agent] + [verb]
受 and 受到 put the subject on the receiving end. What follows is a two-syllable verb treated as a thing received: 欢迎 "welcome", 影响 "influence", 表扬 "praise", 批评 "criticism". It's neutral to written.
The person doing it goes in as a 的 phrase before the verb: 老师的表扬, "the teacher's praise".
受 itself can take a degree adverb, which a plain verb after 被 can't. 很受欢迎 is the everyday way to say "popular".
被 takes a full verb phrase: 他被老师表扬了. 受到 takes a noun-like verb with nothing after it. Use 受到 for praise, support, attention and welcome; use 被 for physical actions done to someone.
受伤 and 受委屈 are fixed words with 受: "get hurt", "be treated unfairly".