Yes, it looks like you need a Twitter account in order to create a Twitter application, but it doesn't have to be an account for your website. For instance, if I want to create a "Sign in with Twitter" button on my, page, I can just log into the dev site using my personal account and create an application. Follow the steps here. In particular following the "application settings" link will prompt you to login, and then you can create an application.
Facebook likewise requires you to have an account and create an application. They then provide API keys that can be used in the OAuth login flow. They have two ways to get a token: a server side flow that provides a longer lived token, and a client side that gives a shorter one. For more details see this page.
With Google, if you use their OAuth 1.0 flow, you can do a login without creating an application (https://developers.google.com/accounts/docs/OAuth). However, it looks like their preferred way is their OAuth 2.0 flow through Google+. See this page.