MySQL-ORをANDに変更

havingで試すことができます ：

SELECT Ads.AdId 
FROM Ads 
JOIN AdsAmenities ON Ads.AdId = AdsAmenities.ads_AdId 
WHERE AdsAmenities.amenities_AmenityId IN (2, 18, 1) 
GROUP BY Ads.AdId
HAVING COUNT(distinct AdsAmenities.amenities_AmenityId) = 3

AdsAmenities.amenities_AmenityIdの場合 値は一意です。distinctをスキップできます 一部。