What is the difference between "outlet" "vehicle" and "avenue"?

According to Lexico Dictionary, the three words are defined as:

1) Outlet

a means of expressing one's talents, energy, or emotions:

Example: "writing became the main outlet for his energies"

2) Vehicle

a thing used to express, embody, or fulfill something:

Example: "I use paint as a vehicle for my ideas"

3) Avenue

a way of approaching a problem or making progress toward something:

Example: "three possible avenues of research suggested themselves"

I'll try my best to state my intentions for asking this question: I came across these 3 words while reading some books and noticed that they seemingly have a similarity--that similarity being "a means of attaining something". I've asked some friends if my analysis is right; all of them say no. So I'm posting this question to get people's opinions on whether I am right on these 3 words sharing a similarity and if my analysis is also correct. If I'm wrong, tell me where my interpretation is wrong.