Puedes probar 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
En el caso de AdsAmenities.amenities_AmenityId
los valores son únicos, puede omitir distinct
parte.