the first detailed mapping was done in 1868 by Ordnance Survey - these maps can be consulted at Manx museum (the fields, roads etc are numbered which refer to a names book also held at museum - I have scans of about 60% of these maps - before this you have the tithe (1830's) and asylum (1860) plans - the O/S was revised in late 1890's but no resurvey was done and wasn't done until the new digital maps were made about 30 years ago.
There may be local plans but these will almost certainly use the O/S maps as base - by late 19th C you can see the use of the O/S base map used to agree property boundaries etc but these would be local copies held by the interested parties.
The Museum can help with maps but they cannot (and will not) enter into discussions as to ownership - they will however point out the interpretations of the name book etc - however I'm sure that any advocate is well aware of the sources needed to prove title.