>Is there a way to sell on eBay without using PayPal?
No, offering PayPal is mandatory for sellers on eBay.
>Also if I want to sell on other sites and post things out to people but don't want to use PayPal, what methods can I use not to get scammed?
Western Union and BACS transfers are irreversible, so you can't get scammed as long as you wait until the payment has cleared; your customers have no protection whatsoever, so they'd have to be a total idiot to get involved. Fortunately for you, there are a fair number of morons out there.
If you hate them that much I would suggest you also shouldn't be using the platform of the company that has owned and operated them for the last 16 years.