Storing your oolong would primarily depend on the roast levels of your oolong.
1. Lightly roasted oolong. Some examples are Taiwan high mountain oolongs like Ali Shan oolong. I had also tried a very high grade (aka expensive ) Tie Kuan Yin from China which is also lightly roasted. I liked these teas. It has a refreshing quality, a nice bouquet of fresh flower aroma with a light lingering sweetness in the aftertaste.
These tea are not meant for aging and need special attention in storing these tea. Refrigeration is a commonly used to keep these tea. I suspect the tea leaves may be placed in the freezer. I had seen, when I was in the Guangzhou tea wholesale centres where high grade Long Qing tea was also kept in deep freezers to maintain the freshness of the tea.
2. Medium to high roasted oolong. I recommend you store them in tea caddies. The popular tinned versions are, to me, very nice oolongs and I keep them in their factory packed tins. Most of these tins are double lidded. It is reasonable air tight. Many of these teas do well with age. They do not ferment like pu erh tea, rather oolong oxidised with time. Old high roasted oolong are very highly sought and are very expensive. Even the older canned versions can cost more than $100 per tin.
3. Specialty oolongs. One of my fav specialty oolongs comes from Hong Kong. Its their 40-hr high roast oolong. The tea taste and aroma is a surprising caramel like. A super tea in my opinion. However, this tea is meant to be drank within a year as the roasted aroma will diminish significantly after a year. Its a drink now tea. In spite of its shorter life span, this is a popular tea among many oolong tea drinkers worldwide. I look forward to going to Hong Kong again to purchase this tea. I may consider freezing some of this tea when I return.