Puoi provare con having
:
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
Nel caso AdsAmenities.amenities_AmenityId
i valori sono uniq, puoi saltare il distinct
parte.