¿Ordenar SQL por LIKE más fuerte?

Si quiere decir que col_1 es más relevante que col_2 y así sucesivamente, entonces:

select *
      ,case when col_1 like '%$keyword%' then 1
            when col_2 like '%$keyword%' then 2
            when col_3 like '%$keyword%' then 3
       end as [priority]
  from table_name
 where col_1 like '%$keyword%'
    or col_2 like '%$keyword%'
    or col_3 like '%$keyword%'
 order by [priority]

Si quisiste decir con la mayor coincidencia de columna, entonces:

select *
      ,(case when col_1 like '%$keyword%' then 1 else 0 end) +
      ,(case when col_2 like '%$keyword%' then 1 else 0 end) +
      ,(case when col_3 like '%$keyword%' then 1 else 0 end) as [priority]
  from table_name
 where col_1 like '%$keyword%'
    or col_2 like '%$keyword%'
    or col_3 like '%$keyword%'
 order by [priority] desc