Don't have an 054 engine, would like to get one, but the track loop is 036. Can an 054 run in a typical loop on this size track? I would only be pulling 027 size cars, so I would think there is no interference there, but can the engine itself make it around,(can the trucks turn that much?). The engine in question would be a cab forward. thanks.
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Not usually, the manufacturers give minimum curve requirements for a reason.
The "O36" is the diameter of the curve, the larger the number the wider the curve.
See here: Lionel Recommended Minimum Curve Info
Rick is right. Most 054 engines won't even run on 042. They just derail.
I wouldn't think so. I think RickO has it right. Some members have reported success when there is just a small difference, but what you propose seems to be quite a stretch, unfortunately.
There's an exception to the rule. MTH O42 track is actually 2" smaller in diameter than is Gargraves. If MTH measured their diameter the same way that Gargraves does, the MTH O42 would be thee equivalent of a Gargraves O40.
After learning this on the forum, I took a chance and purchased an MTH Premier Swiss Crocodile, listed as requiring O54 curves. It runs just fine on my Gargraves O42 loop. However, it needs every bit of that O42 diameter.
Since MTH typically lists the minimum curves of their engines as the smallest diameter curve of MTH track that it will negotiate, some MTH engines rated O54 will actually negotiate other manufacturer's O42 curves.
One off the all example is my MTH Premier ALP-36. It's rated O72, however, it negotiates my Gargraves O42 very well, as long as it doesn't have to go through the curved portion of a Gargraves or Ross O42 turnout. The Swiss Crocodile also won't negotiate the curved portion of those O42 turnouts.
I have run, with no problem GG1 designated for 042 minimun on 036, and several steam locos on 042 designated for 048 with no hitch under the xmas tree several times. But trying something designated for larger radius, no.
And besides mechanical, there is the asthetic looks with a big overhang (and bumping adjacent structures) and trucks swiveling way out on curves. Had a nice set of passenger cars I returned after seeing how bad they looked going around O-42s. A set of O-27 baby Madisons solved that problem though not in my roads name 
Will O54 locomotive operate on O36 or O31?
Short answer: No!
In some instances a locomotive designated for a certain minimum diameter curve may negotiate the next smallest size down (in this case it would be O42 or O48, depending on type of track), but whether it will properly track cars attached to that engine is another matter altogether.
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