I'll try to expand this a bit for clarity.
Let's limit the question to before the migrational period. I'm thinking more along the lines of the Gauls sacking Rome, Boudicca, Vercingetorix, Arminius, that sort of era. I know Arminius had quite good organization, but he was trained by Rome, so I'm thinking more along the lines of how the native "barbarians" would have behaved in combat. I also know this is still a fairly long period in question, but I can't think of any way to neatly divide it further.
Maybe more specific questions could be attempted such as:
In battle, is there any indication that they had a command structure, and an ability for leadership to make large scale maneuvers to defeat an opponent, rather than just rely on sheer numbers to grind them away?
Is there any indication that they had the strategic and logistical capacity to wage campaigns over an extended period, and effectively manage supplies to sustain a large force?
I recognize that these could be very difficult questions to answer due to lack of sources, so even if they cannot be answered completely, I would appreciate if anyone attempted it to the best of their ability.
Thank you all.
The answer is yes, the Celts for example displayed great tactical ability, I will quote myself on an earlier reply to a similar question:
"The Celts also formed the Kingdom of Galatia in Modern Turkey despite resistance from successor states, conquered Macedon and sacked it's most holy sites and famously repeatedly sacked Rome. The Celts were an incredibly successful civilisation or cultural group. Why is a matter of some debate, some like Peter Berresford argue that Celtic expansion was due to the highly developed military system of the Celts who were able to produce weapons of a high quality (indeed the earliest and highest quality Iron work seems to have been pioneered by the Celts as seen in the La Tene swords) and that their armies had more members who had seen combat and had perhaps received some basic training. This notion originates from the custom of minor tribal conflicts and near ritualised skirmishing between sub tribes or family dynasties and also games and fairs based around activities that simulate combat (athletic contests, javelin throwing, hunts etc.) we also have record of Germanic Celts banning obesity as it made a man weak for combat.
In most conflicts of the early Celtic era the Celtic armies would be facing armies composed mainly of drafted soldiers who had never seen combat before (as for example the Greek polis hoplite armies) whereas the Celts opposite them would have been familiar with at least some level of combat which is rather helpful.
The Celts from Roman, Greek and Macedonian record also seem to have mastered psychological warfare, Celtic warriors are described as fearless, men in the prime of size and strength stripped naked and screaming challenges might be placed in positions of high visibility but perhaps the most terrifying thing about he Gauls as Livy repeatedly mentions is the sophistication and order of their armies, he notes several times the well formed lines and ability to manoeuvre of the Gallic army at the Battle of Allia and also notes that the Romans were shocked and caught unprepared by how fast the Celtic army had moved suggesting efficient and sophisticated marching and supply at least relative to contemporaries."