Você pode tentar
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
No caso de
AdsAmenities.amenities_AmenityId os valores são uniq, você pode pular o distinct papel. 
