For fuller context, here is the vingette in which the (only) reference to "sidehill garger"—or to sidehill or garger separately—in William Long, Wood-Folk Comedies: The Play of Wild-animal Life on a Natural Stage (1920) appears:
I remember once when they [fox hunters] were swapping yarns, of breaking rashly into the conversation to tell of a fox I had seen in a lucky moment when he did not see me. He was nosing along the edge of a wood, and I threw a chunk of wood after him as he moved away. It missed him by a foot, and he pounced upon it like a flash as it went bouncing among the dead leaves.
Now that was perhaps the most natural thing for any hungry fox to do, to catch a thing which ran away, instead of asking where it came from; but the veterans received the tale in grim silence. One told me that I had surely seen a "sidehill garger"; another wished he could have seen it, too; the rest pestered me unmercifully about the beast all winter. One of them is now in his dotage; but he never meets me without asking, "Son, did that 'ere fox really run arter that chunk of wood you hove at him?" And when I answer, "Yes, he did, and caught it," he says, "Well, well, well!" in a way to indicate that he has been straining at that gnat for forty years.
Long was a clergyman from Stamford, Connecticut, but he spent his summers every year in Maine (or, later, Nova Scotia), and that may be the home of the fox hunters who said things like "arter" and "that 'ere fox" and "sidehill garger."
Google Books and Elephind searches don't turn up any other instances of garger—sidehill or otherwise. But they do find multiple instances of "sidehill [or side-hill] gouger" and one of "sidehill gauger." The earliest match comes from "In Lighter Vein," in the Minneapolis [Minnesota] Journal (January 25, 1902):
"Side Hill Gougers."
When the Great Northern was building through western Montana in the early nineties there was a very green Englishman in one of its surveying parties. For his edification the boys in the camp talked much of "side-hill gougers" in the mountains. To the Englishman it was explained that the side-hill gouger was a peculiar sort of bird that lived in the mountains, and from long acquaintance with side hills had developed a right leg that was much longer than the left. If you could only make the "gouger" run up hill or down hill or the wrong way around the hill, you could catch him. The Englishman, though he watched for every opportunity, never got a chance to try catching gougers.
But an anonymous article titled "The Old Trail: A Winter in the Woods," in Canada: An Illustrated Weekly Journal for All Interested in the Dominion (February 15, 1908) disputes the characterization of the creature as a bird, arguing instead that it was some sort of quadruped:
Superstitions were dear to the heart of the Frenchmen [that is, Quebecois]. Their belief in the all-powerful "Wendigo," whose footprints could plainly be seen after each heavy fall of snow, was not to be shaken by pointing to by pointing out that these same depressions were caused by the falling of masses of snow from overladen branches; while the even more fantastic "side-hill-gouger," a creature so unfortunately equipped by nature that it could only progress on the steepest hillsides owing to its legs on one side being so much sorter than on the other, was a lurking terror at nightfall, strenuously denied, but dimply feared.
And from "The Side-Hill Gouger," in Purdue Debris (1909) [combined snippets]:
Long ago, before the flood, there lived on cone-shaped peaks and in the craters of volcanoes strange beasts. Their bodies were rigid, covered with scales of steel, and they had tails like rabbits and snouts like steam shovels. So rigid were they that they could move on one degree of curvature only, and they dared not look back lest they die. Hence the could go neither up nor down, but only round and round. To accommodate their movements to the hills, their nigh legs were longer than their off ones and those inside the crater were water-jacketed on account of the great heat. The outside gougers moved clockwise, and their mirrored counterparts on the inside moved counterclock-wise. Their food was quartz crystals and many hitherto inexplainable terrace-like formations are now thought due to their metabolism, ...
The earliest three matches for the term thus come from Minnesota, western Canada, and northern Indiana.
Two other other fairly early references emphasize the crucial role that having a credulous listener played the tales about the sidehill gouger. From Gorton Carruth, "Strange Animals," in Youth's Companion (1922):
After a considerable pause Jim looked up from his plate. "Eben," he said casually, "did I tell you I saw gouger tracks over in the south meadow next the woods yesterday?"
"Gouger?" queried Alan. Doesn't Jim men cougar, uncle?"
"No Alan," his uncle answered quietly. "Gouger is right. It's a different sort of animal from the cougar. Guess there aren't any cougars around here any more. No; Jim means gouger right enough—sidehill gouger; that's the critter's full name. I suppose he was headed south, Jim?"
"Sure," answered Jim. "He was traveling easy. He won't be back for a good while. It's a long way round the range. Still, there may be others follering him."
And from Benjamin Mitchell, Trail Life in the Canadian Rockies (1924) [combined snippets]:
Apropos of side-hill gouging, the guides and horse wranglers hereabouts are fond of filling the ears of tenderfeet with tales of a wonderful creature, the side-hill gouger, which for ages had traversed the mountains in only one direction, until, in the course of revolution, the legs on one side of him have become much shorter than the opposite pair. Now the side-hill gouger's flesh is most delicious; and to get him all that is necessary is to head him off. He turns; his short pair of legs find themselves on the down hill; he falls helplessly and is an easy prey. Crude enough, of course. But I have actually seen the impossible tale believed, gulped whole, by those who should have known better.
Mitford Mathews, A Dictionary of Americanisms on Historical Principles (1951) reports that beasts of the same general description as the sidehill gouger have answered to various names and go back to the middle 1800s at least:
sidehill n. ... 2. In the names of, or with reference to, fabulous creatures especially adapted for travel on hillsides, as (1) sidehill critter, (2) dodger, (3) gouger. Cf. prock [defined as "A fabulous quadruped having two short legs opposite two long ones, so as to be able to browse on mountain sides," with citations dating to 1840]. (1) 1849 WILLIS Rural Letters 93 It's a side-hill critter! Two off legs so lame she can't stand even. [Other cited instances omitted.]