All types of teas-white, green, black, oolong - are made from the same tea plant, Camellia sinensis. While the variety of the plant species, cultivating conditions, processing of the leaves, taste and aroma vary among these teas, all of them contain caffeine.
Caffeine Comparison in Oolong, Green, White and Black Tea
The caffeine content of oolong tea is approximately 37 mg per 8 fl. oz. The shape of the tea leaves and brewing methods also affect the amount of caffeine in oolong.
The brewed oolong tea leaves can be used again to make 2-3 more cups of tea. Obviously, the first cup of oolong tea will contain greater amount of caffeine than the later cups. 
The caffeine content in teas is often explained with reference to the fermentation process in tea production. Oolong teas are only partially oxidized while black teas are fully oxidized. On the other hand, oxidation is bypassed during the processing of green teas.
Because of this, the caffeine content of green teas are comparatively lower than other teas such as oolong and black tea. Among these three types of teas, black tea is the most processed tea and contains the highest caffeine content.
This places oolong mid-way between less caffeinated green teas and highly caffeinated black teas which means that the caffeine content in oolong tea is greater than green tea and lower than black tea. 
White teas are not processed as much as other teas. So, it retains the highest amount of caffeine among these four teas. The caffeine content of white tea ranges from 15-75 mg per 8 oz. cup.
Caffeine Content in Different Teas
|Tea||Size in fl. oz.||Caffeine Content|
Source: Caffeine Informer 
Side Effects of Caffeine
There are a few drawbacks to excess intake of oolong tea. Most of these side effects are caused because of the tea’s caffeine content.
Caffeine is a stimulant and excess intake of oolong tea can cause caffeine overdose in your body. This causes increased urination, convulsions, muscle twitching, dizziness and vomiting.
Caffeine can also cause other abdominal problems like diarrhea and constipation. It can be especially harmful during pregnancy. So, pregnant women should limit their daily oolong tea intake to under 4 cups.