SELECT 
  * 
FROM 
  cscart_logos 
WHERE 
  IF(
    layout_id = 0, 
    1, 
    IF(layout_id = 10, 1, 0)
  ) 
  AND IF(
    style_id = '', 
    1, 
    IF(style_id = 'Byggbay', 1, 0)
  ) 
  AND company_id = 2

Query time 0.00142

Explain
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE cscart_logos ALL 75 Using where

Result

logo_id layout_id company_id type style_id
70 0 2 gift_cert
76 10 2 theme Byggbay
77 0 2 mail Byggbay
78 0 2 gift_cert Byggbay
79 10 2 mail Byggbay
80 10 2 favicon Byggbay