At a time when finding genuinely odd places to go on holiday is becoming ever more of a challenge, it’s reassuring to know that one of the world’s most unusual and frankly peculiar destinations lies only an hour’s flying time from Britain’s northernmost tip. Iceland, home of my inlaws, has Europe’s largest waterfalls, glaciers and – yes – deserts, and a population the size of Ealing’s who grow taller, read more and shop harder than any other. And who, in 53 per cent of cases, believe in elves.

I visit the country often enough to know most Icelandair stewardesses by name, and be able to whisper “I am postman of the year” in their native tongue, yet their home-land never gets any less weird. The road to Reykjavik from the airport traverses a moonscape of spiky black lava – reminding me why Nasa sent the Apollo astronauts here to acclimatise – and is distantly flanked by the steaming chromed towers of the Blue Lagoon, where bathers wallow in the outflow pools of a geothermal power station. Then it’s up to my wife’s parents’ place in the city’s ever-expanding suburbs, to watch my father-in-law settling down to a bowl of soured whey mixed with orange juice and a splash of cod-liver oil.

Be sure to visit one of Reykjavik’s many open-air hot baths. Icelanders have been lolling in geothermal pools since the Vikings arrived in 874AD: Reykjavik means “Smoky Bay”, a reference to the wisps of steam they saw as their longboats came up the coast. I can always spot a tourist, being harangued by the attendant for doing what I did on my first visit: failing to strip naked and scrub that filthy foreign bottom with bactericidal soap before entering the water. In summer, you’ll be splashing about in bright sun at 10.30pm; in winter, when daylight is a couple of hours of desultory dawn around noon, snowflakes melt on your nose as you broil in a 40C hot pot.

Two thirds of the population lives in the capital, and with the balance concentrated in the fishing ports that dot the coastline, the interior is a wind-swept, treeless wilderness. It’s also where Iceland comes alive. Travelling through this landscape – bald, dark, Tolkienesque mountains you could climb and be the first to do so, deafening waterfalls, savage rifts and gorges – is awesome and often petrifying. A volcano erupts somewhere almost annually, with earthquakes even more commonplace. Iceland is the newest country in the world, an unfinished corner of the universe still in its geological adolescence.

Don’t look where you’re going in the English countryside and you tread in a cowpat; here you disappear down a glacial crevass. Get lost in the English countryside and you miss last orders; here you freeze to death up an unknown mountain and have the trolls pick at your bleached bones.

If you can face hiring a car (even a tiny Daihatsu can cost £80 a day), drive to Kaldidalur, an Arctic desert strewn with huge orange boulders. If you can’t, catch the Golden Circle bus trip, which takes in Geysir – home of the eponymous phenomenon – and Gullfoss, a majestic two-tier waterfall that ices up in winter for the ultimate freeze-frame. In a land where the extraordinary is the norm – smoked puffin breast with blueberry sauce, a Mother Christmas who eats naughty children – the oddest thing about Iceland is that anyone still lives there.

You wonder how these very modern Europeans, with their hydrogen-powered buses and world-conquering levels of broadband penetration, can tolerate this wind-torn wilderness. The answer is that while in some ways Iceland is a quintessential 21st-century nation, in others it’s still rooted in the 9th. All Icelanders can trace their lineage back to the Viking settlers, and the language has evolved so little that schoolchildren read the sagas in their original form.

So when an Icelandair flight lands in Keflavik, the stewardess’s announcement “Velkominn heim” means more than welcome home – it’s a reminder to all those wandering Vikings that they’re back where they belong.

Times recommends

• Oasis of the Seas: the Times review
• The 20 best new year party places to stay
• Green Spaces 2009: are you the winning writer?