:Search <pattern1> //will highlight all occurences of <pattern1> in the current buffer.
A subsequent :Search <pattern2> will highlight all occurences of <pattern2> in the current buffer.
My Mark plugin can highlight several words in different colors simultaneously, like the built-in search. It comes with many mappings and commands, allows to persist the patterns, and supports multiple color palettes.
There are two simple ways to highlight multiple words in vim editor.
Go to search mode i.e. type '/' and then type \v followed by the words you want to search separated by '|' (pipe).
E.g.: /\vword1|word2|word3
Go to search mode and type the words you want to search separated by '\|'.
E.g.: /word1\|word2\|word3
Basically the first way puts you in the regular expression mode so that you do not need to put any extra back slashes before every pipe or other delimiters used for searching.