Well, "The Germanic Tribes" covers a lot of people over a long time in a large area. And unfortunately a lot of them weren't big on writing, which makes being very certain about the fine details rather difficult. That said, the oldest old Germanic language that we know very much about is Gothic. It's an East Germanic language, and there is a surviving copy of a bible from the 4 Century CE in the Gothic language which helps us understand a lot. Unfortunately, we don't have as good an example of any other nearby East Germanic language as far back to really nail down exactly how similar they were. But they did have an effect on later languages, and some words like old names of things are still known. Today tenacious linguists can piece together quite a lot about those old languages even if nobody is definitely fluent in them any more. We know enough to classify them into various distinct families and such. Wikipedia isn't really a great source, but here's a list of Germanic languages:
https://en.wikipedia.org/wiki/List_of_Germanic_languages
As you can see there are oodles of old Germanic languages, many of which you've probably never heard of. We know at least enough about each of them to say that each and every one are all distinct languages that aren't mutually intellegible. At least not fully. Some will be closer than others.
Old English dates back to nearly as far back as that Gothic Bible. The Lord's prayer in Gothic starts, "Atta unsar þu in himinam" but in Old English it's "Fæder ure þu þe eart on heofonum;" So there are certainly similarities, but it's different enough that I wouldn't expect they'd immediately understand each other without some effort with different vocabularies, accents, and grammars.
Like /u/salientsapient already discussed, there were the East Germanic speaking Goths which spoke a related but different language variety to the West Germanic speaking tribes. So while there were may have been enough similarities to satisfy your definition of "similar", it still would have been at least partially if not mostly mutually unintelligible. Another dimension which meakes this a little hard to answer is that not every germanii tribe may have actually been germanic. The Romans seem to have used it as a catch all for all the native inhabitants north of the Danube and east of the Rhein, as Tacitus seemed to have. Even the name "germanii" may have come from a specific celtic group. However, any of the germanic groups that were descended from the Jastorf culture are probably what you're thinking of here, and yes they should have been able to communicate with each other with great ease for the duration of the existence of the Roman Empire.