In very general terms...
In the pre-Christian Germanic Kingship system the King/tribal chief acted as an equivalent of a high priest and would officiate at ceremonies such as animal sacrifices.
The authority for this came both from the high office held and from claims of legitimacy through inheritance - for example the Anglo-Saxons Royal lineages who settled the British Isles often had mythological genealogies which traced back to Woden
Otherwise there was not a specific class of people who would be described as 'priests' rather the person with the highest social status at a ceremony would take on that role.
Tacitus wrote about the distinction between Celtic and Germanic religions and noted the absence of a priestly class amongst the Germanic peoples.
http://en.wikipedia.org/wiki/Germanic_king
http://en.wikipedia.org/wiki/Anglo-Saxon_royal_genealogies
http://en.wikipedia.org/wiki/Norse_rituals
http://www.fordham.edu/halsall/source/tacitus1.html
However, there are hints in Old High German (spoken from the 5th c. AD) that there were words denoting persons who interpreted oracles, persons who officiated at sacrifices etc. amongst Germanic tribes before the influence of Christianity. These OHG words have a mixture of Latin and older Germanic roots. So the possibility remains open that individual tribes differed from the findings of Tacitus and did have priests - although it's ambiguous as to whether these words, prior to Roman an Christian influence,, denoted a 'professional' priest or simply a person who takes on a role for a event.
Well it depends upon what you refer to as "germanic tirbal society." During the roman periods accounts are sketchy with regards to what Germanic society was truly like. Often times almost all non-Roman Europeans were simply referred to as "Celts." Celts in general are notable for the lack of any clear priestly class as the Romans would define.
Now understanding this we also need to appreciate how incredibly bad roman sources are in general at describing other cultures. Tacititus was simply aggregating second hand experiences with "Celts" who had been brought to Rome.
Archaeological evidence points to a consistent celtic religion that featured holy sites, sacrifices, etc.. What is unclear is whether there were specific people who administered religious rites. The simple answer is that we don't know. It is highly likely that they did have specific people who were tasked with carrying out sacrifices and the like, but we have no way of knowing. The culture had no writing and was utterly wiped out.