Sounds more like the males in your household just have bad 'aim'.

How do you know the toilet is leaking? Is there actually a puddle coming from the base? I agree that it's more likely to be a case of bad aim, particularly if the "leak" is on the front side. In addition, even if you had a leak, the urine would be very much diluted in the bowl before flushing and not likely to produce the strength of odor you are noticing. Unfortunately, if the base of the toilet is not caulked, the externally applied urine may have seeped under and you will probably continue to get some odor even after cleaning.

Do you have indoor pets? We have caught our little dog marking the base of our toilet before.

I had a toilet that had a cracked trap. Couldnt see it from the top. It leaked enough to get past the sealer.

Thanks for all the suggestions. We still think the toilet is leaking from somewhere, but we've attributed the smell to our son's probable bad aim. We're going to try putting food coloring in the bowl and tank to see if that will help us pinpoint the leak.

If you do have a leak, it might be minor enough that food coloring will not show up. Food coloring is used to check leakage of the flapper valve between the tank and the bowl of a 2-piece toilet...not leakage at the wax seal. One thing you could try is hold the handle down for several minutes: this would run a lot of water through the trap at one time and you might see if there is any flow from under the toilet. If you replaced the wax ring previously, I'm still betting on junior as the source of the "leak"....

"Is there a way to check the subflooring to see if it's wet without damaging the linoleum?"

You have a crawl space under the subfloor. Go down there and check.

I think it's an aiming issue too. The urine is diluted in the water, so if you are finding yellow urine around the base of the toilet (which I often do) someone is missing!

Whenever we find small amounts of water on the floor near the base of a water closet we instantly think either the fixture is leaking or someone has a bad aim, but there is another, although rare, source of water which has not been mentioned.

During periods of high humidity when a water closet is flushed the new water entering the tank cools the tank sufficiently to cause moisture from the surrounding atmosphere to condensate on the tank. In a worst case scenario you will see large droplets of water formed on the underside of the tank but sometimes the amount of condensate that forms is so slight as to go unseen. The condensate clings to the surface of the bowl in slightly more than a molecular layer and slowly flows down to the floor by surface tension. When this occurs it can be detected by wiping the underside of the tank or the back of the bowl with a dry tissue.

If you determine that you are getting condensate moisture on the fixture there are a number of corrective actions that you can take.

1.Increase the operating time of your exhaust fan to reduce the amount of humidity in the room air.

2. Install an insulation jacket on the inside of the water closet tank or install an insulated tank. (nearly all water closet manufacturers now offer insulated tanks as an option)

3. Install a mixer on the tank water supply line that mixes a slight amount of hot water with the cold water to maintain the tank at room temp. (special mixers are available for this application).

I have darn-good, spot-on aim and my sister cleans the toilet whenever the "leak" starts to become noticeable. It only occurs around the little screws where there is a space or whatever. And then it spreads outward and I'm pretty smart and if it were my fault then it wouldn't start at a certain point and then spread outward- it would be random urine everywhere around the base lol

And that is a definite maybe!

I have that problem, but only on the sides. I can tell it's not "bad aim"

And there's always this decal: