SELECT 
  * 
FROM 
  cscart_logos 
WHERE 
  IF(
    layout_id = 0, 
    1, 
    IF(layout_id = 3, 1, 0)
  ) 
  AND IF(
    style_id = '', 
    1, 
    IF(style_id = 'mnm', 1, 0)
  ) 
  AND company_id = 1

Query time 0.00025

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "3.66"
    },
    "table": {
      "table_name": "cscart_logos",
      "access_type": "ALL",
      "rows_examined_per_scan": 31,
      "rows_produced_per_join": 3,
      "filtered": "10.00",
      "cost_info": {
        "read_cost": "3.35",
        "eval_cost": "0.31",
        "prefix_cost": "3.66",
        "data_read_per_join": "818"
      },
      "used_columns": [
        "logo_id",
        "layout_id",
        "style_id",
        "company_id",
        "type"
      ],
      "attached_condition": "((`maniamall_cscart`.`cscart_logos`.`company_id` = 1) and (0 <> if((`maniamall_cscart`.`cscart_logos`.`layout_id` = 0),1,if((`maniamall_cscart`.`cscart_logos`.`layout_id` = 3),1,0))) and (0 <> if((`maniamall_cscart`.`cscart_logos`.`style_id` = ''),1,if((`maniamall_cscart`.`cscart_logos`.`style_id` = 'mnm'),1,0))))"
    }
  }
}

Result