What words sound like opposites but are synonyms?
- regardless and irregardless (although some don't consider irregardless a real word)
- bone and debone
- press and depress
- caregiver and caretaker
- ravel and unravel
some related examples in slang. These use the same word, but mean the opposite:
- shit and the shit
- bollocks and the bollocks, or the dog's bollocks
- a bomb and the bomb
Valuable and invaluable is the only example that comes to mind
http://grammarist.com/usage/invaluable-valuable/