The first recorded instance of a building made specially for Squash was in 1864 at Harrow, England when four courts were erected.  These were built on the site of the previous open-roofed "ad-hoc" courts.

The first ever privately owned Squash court was built by a former Harrow pupil, Vernon Harcourt, in Oxford in 1883.

The first recorded Squash court in the USA was built by the Philadelphia Racket Club in 1891.

The first attempt to standardise the size of the international squash court was by the Tennis and Rackets Association (UK) in 1909.  It failed.

A successful attempt to standardise courts was made in 1925 by the Tennis and Rackets Association.  The following were the dimensions chosen:

The Service Box shall be entirely enclosed on three sides within the Court by lines, the short line forming the side nearest to the front wall, the side wall bounding the fourth side.  The internal dimensions of the Service Box shall be 5 feet 3 inches.
All dimensions in the Court shall be measured, where practicable, from the junctions of the floor and front wall, and to the further edge of the line to be demarcated.
The lines marking the boundaries of the Court shall be 2 inches in width.
The width of other painted lines shall not exceed 2 inches.
All walls shall be white.  The space below the board shall be white.  All lines shall be coloured red.
The front wall shall be composition.
The side walls and back wall shall be of wood or of composition.
The floor shall be of wood for covered courts and of composition for open courts.
The Board and the space below it to the floor, and the area above the height of play on the back wall should be constructed of some resonant material.

The first glass backwall to be installed was at the Abbeydale Club, Sheffield, England in October 1969 by Ellis Pearson Ltd.

The first use of a portable court for a major championship was in September, 1978 in Kings Hall, Stockholm, Sweden on the occasion of the Swedish leg of the PIA World Series.  Perstop Ltd. erected a prefabricated court with a glass backwall in the arena.  Some 600 people watched the final.

Whilst Squash has had its share of variants in playing (mainly by placing obstacles in various places, notably the back corners) the strangest racket game we have met is (or was?) called "Smacquetball"!  It is played on a racquetball court, and each player has two fibreglass-reinforced nylon "hand racquets", one strapped to each hand.  There are no backhand strokes.  The comment made was "how do you pick up the ball"?

From an actual real-estate advertisement:

About the house
Yes, it really was a squash court -- it was built in the early 20th century for the Marquis of Camden, who lived in the mock-Jacobean mansion that still stands several hundred yards to the south. Converted to a house in the 1970s, the Old Squash Court has been completely refurbished by the present owners over the last ten years.
Detached, brick-built house 
Large, double-height loft-style living room 
Spacious open-plan country kitchen-dining room with Aga 
Four bedrooms 
Two bathrooms 
Utility room 
Garage 
Professionally-landscaped gardens of two-thirds of an acre 
Guide price £345,000 freehold
(including internet domain name)
The Location
The Old Squash Court is conveniently located on the Kent/East Sussex borders, roughly half way between Tunbridge Wells and Lamberhurst. The M25 is about 20 miles away along the A21, which passes about three miles to the east of the house.

A pretty expensive ex-Squash Court  --  Any Offers?

Persian carpets: all sizes, old and new, from Iran, Turkey, Afghanistan, and China. This is the very best time of year to obtain the lowest prices. Reductions on everything ahead of new autumn consignments. Browsing encouraged. Goods on approval. Also first-class repairs and cleaning. Usual business hours 10 a.m.–6 p.m., Mon.–Sat. Ring first before traveling any distance or just drop in if passing. Old Squash Court, 16 Linton Road, North Oxford. Tel.: Oxford 559396. (Can anyone take a picture for me?)