Conversion failed when converting date and/or time from character string

You'll need to divide your ORDER BY into multiple CASE statements:

ORDER BY 
    CASE WHEN @orderby = 0 THEN news_edits.[time] END DESC,
    CASE WHEN @orderby = 1 THEN news_edits.lastedit END DESC,
    CASE WHEN @orderby = 2 THEN news_edits.title END DESC

This is because single CASE statement requires that all branches have compatible data types. Since your character string in one CASE can't be converted to the date time returned from another CASE, you get the conversion error.