Oliver's described as having a nose like an elephant's trunk—long and flexible. Like an elephant sniffing out for food, Oliver's always sniffing out for new opportunities, in this case opportunities for social advancement. Despite being the richest jeweler in England, Oliver lacks social status, a situation he hopes to remedy by entering into a sordid little bargain with the Duchess.
Along similar lines, Oliver's likened to a giant hog in a pasture filled with truffles. Truffles are a kind of fungi, arguably the most expensive food in the world. They're located by using pigs, whose superior sense of smell draws them to these delicacies, which often lie buried deep in the forest undergrowth.
Again, the comparison with Oliver is entirely appropriate. He has the remarkable ability to sniff out opportunities, with each opportunity (each "truffle," if you like) being more promising than the last. The rich earth of Mayfair, a very fashionable part of London, is Oliver's hunting ground: the ideal place for this truffle hog to uncover new opportunities for social advancement.