Faulkner was great at it but it was accent he grew up with the accent he used and being Faulkner I think it fair to assume he had a little more talent than the average Marvel writer.
I haven't seen Deadpool yet, maybe this weekend, so I don't know how bad the accent is but what I do remember is his Russianness was more pronounced than some of the other character's foreign origin. He used Russian words the average American kid would recognize from James Bond movies like Neyt and Da and talked about being a peasant. Storm was from Africa but you would never know it from the way she spoke. Rogue called everyone Honey so you would know she was from the south but that is all I really remember. Keep in mind back in the 70s these books were still being written for kids.
In general Marvel was bad at accents and much like the character's back stories they drifted depending on who was writing them. I don't what the final count on Wolverine's back stories is at but when I was reading them Sabertooth was his father and he was not hundreds of years old. I do think your assessment of Wolverines toughness leaves out the fact that while he does regenerate his still feels pain like anyone else. It may be easier to be brave when you know you can't dies but it does take brass balls to jump in the fight knowing you are going to flayed alive yet again.