You mention an ablative absolute in your question; hac oratione is not part of an ablative absolute, though you're obviously right that it is in the ablative.
Let's start from the beginning, though. If we look for the main verb, we see there are two indicatives in this sentence (dant and sperant) and an et after the first one, so this looks very much like two sentences joined together. Taking just the first one:
Hac oratione adducti inter se fidem et ius iurandum dant
The main verb is clearly dant, a 3rd person plural. If the subject is expressed, it will be in the nominative plural.
Adducti is a perfect passive participle and could formally be a genitive singular (masculine or neuter), or it could be a masculine nominative plural. Does the sentence make sense if you read it as the subject of dant? (It should, because it is.)
Adduco can mean a few things, but in this case it probably makes the most sense to read it as 'persuade' or something similar.
Hopefully that clears up the construction. If not:
Hac oratione is an ablative of means that goes with adducti: 'those who were persuaded by this speech'.
My very literal translation of the whole thing:
Those who were persuaded by this speech give pledge and oath to one another, and hope to, having taken possession of power, be able to, through the three very powerful and strong peoples, take possession of the whole of Gaul for themselves.
(Note that regno occupato is an ablative absolute.)
