You should use small caps "or" and "and" instead of OR and AND.
And beware also the spaces/tabs between keywords and arguments (you need at least two spaces).
Here is a code sample with your three keywords working fine:
Here is the file ts.txt:
*** test cases ***
mytest
${color} = set variable Red
Run Keyword If '${color}' == 'Red' log to console \nexecuted with single condition
Run Keyword If '${color}' == 'Red' or '${color}' == 'Blue' or '${color}' == 'Pink' log to console \nexecuted with multiple or
${color} = set variable Blue
${Size} = set variable Small
${Simple} = set variable Simple
${Design} = set variable Simple
Run Keyword If '${color}' == 'Blue' and '${Size}' == 'Small' and '${Design}' != '${Simple}' log to console \nexecuted with multiple and
${Size} = set variable XL
${Design} = set variable Complicated
Run Keyword Unless '${color}' == 'Black' or '${Size}' == 'Small' or '${Design}' == 'Simple' log to console \nexecuted with unless and multiple or
and here is what I get when I execute it:
$ pybot ts.txt
==============================================================================
Ts
==============================================================================
mytest .
executed with single condition
executed with multiple or
executed with unless and multiple or
mytest | PASS |
------------------------------------------------------------------------------