What I have seen
twice, however, is an orange male House Finch.  I have no idea what he is
eating, or where he is eating it, to account for the different coloration.
  Does anyone know if this would have been the result of his summer diet?

Holly-

This is  caused by eating introduced honeysuckle. 
I have seen it on finches, eye line on 
White-throated sparrows (usually yellow), and 
belly feathers of Veery as well as tips on waxwings.

Cedar Waxwings with orange instead of yellow tail 
tips began appearing in the northeastern United 
States and southeastern Canada beginning in the 
1960s. The orange color is the result of a red 
pigment picked up from the berries of an 
introduced species of honeysuckle. If a waxwing 
eats the berries while it is growing a tail 
feather, the tip of the feather will be orange.

 From the Birds of North America account for house finch:

Yellow/orange/red color of feathers results from 
deposition of 3 carotenoid pigments: ß-carotene, 
which produces yellow to orange color in 
feathers; isocryptoxanthin, which produces orange 
color in feathers; and echinenone, which produces 
red color in feathers (Brush and Power 1976). 
Controlled feeding experiments with captive House 
Finches indicate that all individuals in all 
populations have same potential to be brightly or 
drably plumaged; variation in color of feathers 
reflects differential access to carotenoid 
pigments at the time of molt (Brush and Power 
1976, Hill 1992, in press a, b). Males from 4 
different C. m. frontalis populations (brightly 
plumaged Michigan, California; drably plumaged 
California, Hawaii) responded to standardized 
diets in a similar manner. When they were fed a 
plain seed diet, which was fully nutritious but 
provides few carotenoid pigments, all males grew 
feathers with similar pale yellow coloration 
(Brush and Power 1976, Hill 1992, in press a). On 
a seed diet with ß-carotene added, all males grew 
pale orange feathers. And, on a seed diet with 
the red carotenoid canthaxanthin added, all males 
grew bright red feathers. Moreover, the variance 
in plumage coloration among males after treatment 
on a standardized diet was significantly lower 
than the variance in appearance among males from 
wild populations (Hill 1992). Female House 
Finches also converged on a similar plumage when 
their access to carotenoid pigments was 
standardized during molt (Hill in press b). 
Although relatively few wild females show 
detectable carotenoid pigmentation (see 
Distinguishing Characteristics), when 
canthaxanthin was added to their diets all 
females showed maximum female expression of 
carotenoids with a red wash on the rump, crown, 
and underside (Hill in press b).

Hope this helps.

Kent McFarland
VINS Biologist