OmniAuth & Octokit.

authentications_controller.rb

class AuthenticationsController < ApplicationController
  # This is the callback method from OmniAuth's GitHub authentication.
  # following http://railscasts.com/episodes/236-omniauth-part-2
  def create
    omniauth = request.env["omniauth.auth"]
    authentication = Authentication.find_by_provider_and_uid(omniauth['provider'], omniauth['uid'])
    if authentication
      sign_in_and_redirect(:user, authentication.user)
    end
    
    # lots more code goes here, but you get the point.
    # It authenticates and I can grab the OAuth token from omniauth['credentials']['token']
  
    # calling a custom method that will later be in the controller, but is instead here to test.
    save_update_to_github
  end
  
  # This should look very familiar.
  
  def save_update_to_github
    # since this is here, I can grab the token directly. Otherwise I'd get it from the DB.
    token = request.env["omniauth.auth"]["credentials"]["token"]
    github = Octokit::Client.new(:oauth_token => token)
    repo = 'mattboldt/blogtest'
    ref = 'heads/master'
    sha_latest_commit = github.ref(repo, ref).object.sha
    sha_base_tree = github.commit(repo, sha_latest_commit).commit.tree.sha
  
    file_name = "test.md"
    blob_sha = github.create_blob(repo, Base64.encode64("some placeholder code, will be a @post param later."), "base64")
    sha_new_tree = github.create_tree(repo,
                              [ { :path => file_name,
                                   :mode => "100644",
                                   :type => "blob",
                                   :sha => blob_sha } ],
                               {:base_tree => sha_base_tree }).sha
    commit_message = "Committed via Octokit!"
    sha_new_commit = github.create_commit(repo, commit_message, sha_new_tree, sha_latest_commit).sha
    updated_ref = github.update_ref(repo, ref, sha_new_commit)
    puts updated_ref
  end
end

omniauth.rb

Rails.application.config.middleware.use OmniAuth::Builder do
  provider :github, 'ID', 'TOKEN', :scope => 'repo,gist'
end

routes.rb

  
  # callback routes that go to authentications controller.
  
  get "/auth/:provider/callback" => 'authentications#create'
  get "/auth/failure" => "authentications#failure"

Thanks for the writeup!
I noticed though, that for the current version of octokit (4.7.0), you'll have to use access_token: token instead of oauth_token.