Scratch the surface of any society and you're almost bound to uncover one or two traces of eccentricity. The apparently staid Germans have their lederhosen; the sombre Norwegians eat half-fermented trout at Christmas and pretend to enjoy it …

However, I had been told that on the Isle of Man no surface scratching was necessary: the populace was so relaxed about the island's manifold quirks and idiosyncrasies that it rather rejoiced in them. Mind you, if your self-governing British Crown Dependency is named after an obscure Celtic sea god (Manannán Mac Lir, since you ask) and your national symbol is a three-legged figure bereft of either body or head, perhaps having a slightly tangential world view comes naturally.

As it was, I experienced some of the Manx take on the world before I'd even set foot on the island, for she had disappeared under Manannán's cloak. Reportedly, the sea god protects the isle from her enemies by draping his cape of mystical mistiness over her so that they sail blithely past. Thankfully, modern navigational equipment is wise to this ruse and my ferry docked safely, allowing me to invade the island, albeit in a mild-mannered touristy way.

The next day, leaving my hotel in Port St Mary, in the south of the island, I took it into my head to visit the 621m summit of Snaefell, Man's highest peak (while desperately holding in jokes about man's highest peak actually being the ceiling of the Sistine Chapel).

I shared a platform of the local steam railway station with a woman who told me she was off doing her weekly shop. This is not anything so contrived as a restored heritage line. It opened in 1873 and has simply never been updated. The narrow-gauge engines and beautiful rolling stock (lovers of polished wood are in for a treat) are the same ones the Victorians used.

So when, at Ballasalla, a guard came through the train announcing: "There'll be a slight delay ... of 30 minutes," everyone in the carriage was having such a nice time that no one even tutted. There's a laid-back culture hereabouts – the term traa dy liooar means "time enough", and it's the Manx equivalent of the Hispanic mañana – whereby a "slight delay" can indeed mean half an hour or more. I was thankful the guard hadn't announced a state of total chaos.

The railway station I needed is on the far side of Douglas, the island's capital, so I naturally boarded a horse-drawn tram for a 20-minute ride along the promenade. It's been going since 1876 and is, unsurprisingly, the oldest operating horse-drawn tram in the world. The service it connects with, the Manx Electric Railway, opened 17 years later. Nothing, as far as I could tell, has changed since.

Can you see a pattern starting to emerge? In my open train carriage we screeched and squeaked and squealed our way along the coast around a seemingly endless succession of bends and a station called Fairy Cottage until we reached Laxey (home of the world's largest working water wheel, a beautiful red-and-white confection looking like a fairground big wheel that has got lost in a wood), where I changed on to the Snaefell Mountain Railway.

This four-mile electrically powered museum-piece assault on the mountain was built in 1895. And no, they haven't thought to alter anything since, presumably because it works perfectly well as it is thankyouverymuch. I'd been told that from the summit I could see Seven Kingdoms on a clear day: Man, England, Ireland, Scotland, Wales, Heaven and Manannan's (the Sea). Sadly, whichever Manx god controls the clouds had contrived to plop one on top of Snaefell: I could barely see seven yards.

Of course, such bad luck could be ascribed to a number of things. I might, for instance, have provoked the mooinjer veggey – the little people – by not greeting them as I passed Fairy Bridge on the main road south from Douglas. My bus driver certainly did. Or perhaps I had used the forbidden word. When I discussed this with a senior member of Tynwald before he showed me around the island's seat of power (which happens to be the oldest continuous parliament in the world), he became noticeably edgy about the possibility of me uttering the banned name of the rodent he resolutely referred to as a "longtail".

I wasn't even sure I was allowed to get ratty about having missed both the World Tin Bath Championships (7 July) and Tynwald Day (5 July). At the latter, under a huge canopy of the sort one usually only sees at jousting tournaments, all the laws created over the past year are read out in English and Manx. Locals assured me this is more fun than it sounds.

I'd also just missed the annual Parish Walk. Anywhere else this would be a pleasant afternoon stroll, perhaps with scones afterwards, but here it involves participants hiking a death-defying 85 miles in less than 24 hours. And no, that's not a typo.

Guiltily, I took the bus back ("hello, fairies!") to my lodgings at Aaron House, where owners Kathy and Reggie greeted me in full Victorian servants' uniform, mob cap and all. This is less surprising than it sounds because what they've created here is an entirely Victorian hotel, complete with an antique brass telescope in the morning room for spying steam ships out at sea. Thankfully, Kathy's breakfasts, though served with Victorian crockery and cutlery, are tasty in a 21st-century way.

Curiously, after a few days on the island, I began to wish that these so-called oddities were a part of my life back home too. For who would not want their working day brightened by a ride on a steam train, or be able to blame anything bad that happens on those pesky mooinjer veggey?

It was the English writer Edith Sitwell who said: "Eccentricity is not, as dull people would have us believe, a form of madness."

Indeed, if the Isle of Man is anything to go by, one could say that it's a sure proof of sanity.

• Aaron House has rooms from £35 per person per night (01624 835702, aaronhouse.co.uk). Ferry travel was supplied by the Isle of Man Steam Packet Company (08722 992992), with fares from Heysham from £18. Train travel was provided by by Virgin Trains (08719 774222), which has advance singles from London to Lancaster from £14; and Northern Rail (08450 000125), single ticket from Lancaster to Heysham Port, £3.60. Information on Isle of Man railways at gov.im/dccl. New last year on the Isle of Man, Manx Litfest, in Douglas from 26-29 September, will feature a schools day, a family day and appearances by former hermit Neil Ansell, local crime writer Chris Ewan and storyteller Ben Haggarty.