I found a discography that says the McNultys recorded a song with this title in 1937, on Decca 12088 B, but I wasn’t able to find a recording, but it seems likely this is the same song:

The following lyrics appear as a poem in Cassell's Illustrated Family Paper, New Series, Vol. 6, No. 151 London: Oct. 20, 1860, page 331, column 2—with the attribution to Ellen Forrester.

THE OLD HOUSE FAR AWAY
Ellen Forrester

1. The wild birds warble; the sparkling rills
Sing cheerily round the spot;
And the peaceful shade of the ancient hills
Falls dim on my mother’s cot;
Its windows are small, and its thatch is low,
And its walls are a dingy grey;
Oh, I see it! I love it! wherever I go,
That old house far away!

2. The little clock ticks on the parlour wall,
Recording the passing hours;
And the pet geranium grows rank and tall,
With its brilliant scarlet flowers;
And the old straw chair, so cosy and low,
Where mother sits knitting all day:
Oh, I see it! I love it! wherever I go,
That old house far away!

3. Dear mother! how plainly I see her now,
Reclining in that old chair,
With the sunset resting upon her brow,
That was once so smooth and fair!
I see her crimp’d border as white as snow,
And her once dark hair now grey.
Oh, my heart is with her, wherever I go,
In the old house far away!

4. Not all the luxuries earth affords,
The riches of land and sea,
Nor all the wealth of earth’s haughty lords
Could blot from my memory
The roof that shelters each dear, dear head;
And that humble floor of clay
Where the feet I love are wont to tread
In the old house far away.

- - -
The poem was apparently set to music by at least 5 different composers:

Sheet music for a version composed by H. Grante, dated 1861, and published by H. M. Higgins of Chicago, can be seen in the Levy Sheet Music Collection at Johns Hopkins University. Edward Fitzgerald is credited as lyricist (erroneously, I think).

A version composed by A. J. Abbey dated 1864 and published by W. W. Whitney of Toledo, Ohio, can be seen at the Hathi Trust. No lyricist is credited.

A version composed by Henry Tucker dated 1876 and published by J. L. Peters of New York, can be found at the Library of Congress. Lyrics are attributed to Edward Fitzgerald.

I have found references to versions composed by J. P. Samuel (Marshall, Mich.: J. S. White & Co., 1867) and by Sir G. A. Macfarren (London: Bowerman & Co., 1896), but I haven’t found digital images of them.