Octavian was engaged in a project to stabilize Roman borders by moving them to natural barriers (and by entering a peace treaty with the Parthians). After the defeat, he had to give up the original plan to push the northern continental border to the Elbe river and had to settle for the Rhine instead. The Rhine/Danube border remained essentially unchanged (+/- Dacia) for the next couple centuries.

While I have no idea how the Gothic migration or the Hun invasion would play out in that scenario, I don't see how the precise placement of the border could have any major consequences before the butterfly effect makes any such counterfactual questions pointless.

On the other hand, the fact that the expansion into Germania failed, marks (except for a brief period under Trajan) the end of the territorial expansion of the Roman Empire and sets off a time where the Empire's territory remained mostly unchanged until the death of Theodosius (except for a brief period during the crisis of the third century). This is off course hugely significant. The Roman Empire conquering Parthia, then India, maybe even China would be a monumental change in world history.

My personal pet theory* is that, although Octavian intentionally tried to stabilize the Roman territory, the true reason for the end of expansion is, that the fall of the Republic created an almost endless string of dynastic struggles triggering an endless string of civil wars, which simply kept the Romans busy.

Every time an Emperor set off with an army far enough to conquer new territory, a rival for power would gain political clout back home during his long absence. Every time he sent a general instead, if victorious, the general would return home to try and depose the Emperor with his now loyal army, triggering a new civil war, loosing the territory in the process.

In that sense, Teutoburg was not the cause, but merely the symptom. Republican Rome would have sent another consul with a new army next year.

There are some obvious problem with that idea: dynastic struggles leading to civil war actually started quite a bit earlier with Marius and Sulla. And then there is Hadrian who ruled uncontested for 20 years and decided to stay home and build some walls.

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* I'm giving you my pet theory here, because by asking for 'repercussions' you are essentially asking: what are the bad things that would not have happened had Varus won instead. This is a counterfactual question, hence speculation.