Bryan,
Forget about the mytical majic formula, and don't expect too much help from the manufacturer, who will tend towards the optimistic in claims.
Experience, through experimentation, will lead to a collection of odour treatments - I carry about ten favourites.
Learn what you can about the cause of individual odours and this enhanced understanding will help you select the most appropriate type of treatment.
The dog odour you refered to, for example, is caused by bacterial decomposition of sebaceous oils from the dogs coat. Treatment therefore should attack the bacterial colony, remove the oil from the carpet by cleaning and treat the room odour that has deleloped from the emanations from the carpet.
This latter element is where the forced ventilation I mentioned comes into play. During the cleaning process an airmover should be employed to expell air from the room to the outside air through a window or door. Failure to do this will lead to the temporary increase in odour from the carpet further contaminating other absorbent surfaces in he room, such as soft furnishings and even wallpaper.
When the carpet clean is completed these secondary (consequential) odour sorces can be addressed by light treatment with an odour neutraliser. This could be in the form of thermal fogging or cold-air misting, where a fine mist is introduced into the output of an air mover. Care should be taken to protect polished wood surfaces as these can be pitted by many odour neutralisers.
John.