I was following the vignette for the package, updated and loaded all necessary packages, seemed like it would be a pretty straight-forward process to authenticate. Instead,
I encountered the same problems, and after so many attempts.
I found this issue https://github.com/geoffjentry/twitteR/issues/90, where 'jrowen' suggested a work-around that solved my problem. The issue apparently is caused by the new httr package, but the work-around is to install the twitteR package from GitHub instead of the cran repository using this command:
devtools::install_github("jrowen/twitteR", ref = "oauth_httr_1_0")
After this, the problem of OAuth authentication error disappeared. Hope this also works for you.