There isn't really any historical information for that period, since Ireland isn't clearly mentioned in Classical literature until Caesar's Gallic Wars, and more useful information isn't available until Tacitus and Ptolemy in the 2nd century AD. Tacitus tells us that the Irish were similar to the British, having 'tribal kings' and 'internal discord', while Ptolemy provides use with a map of tribes and places. These tribes include the Woluntioi who, given their name and location, can reasonably identified with the ancestors of the Ulaid. But how much of this information can be pushed back into the Hellenistic period is debatable.

As for archaeology, the period of roughly 400 BC to the turn of the millennium is sometimes known as the 'Developed Iron Age'. There is little evidence of settlement during this period, though presumably it followed the later Iron Age pattern of dispersed unenclosed farmsteads, and much of the population may have been semi-nomadic. Some aspects of Bronze Age society, like the occupation of hillforts and use of ceramics, were abandoned. There is, however, abundant evidence of social complexity in the form of La Tene artwork in metal and stone and the construction of major ritual sites and earthworks, particularly at the 'royal sites' like Emain Macha, Tara, Knockaulin and Rathcroghan as well as the series of linear earthworks known as the Black Pig's Dyke which stretch across the northern midlands. Though older interpretations drawing on mythology have sometimes imagined these to be the produce of ancient kingdoms, such earthworks seem more likely to have been the products of communal cooperation between relatively small tribal groups, symbolising regional identities and enhancing social cohesion, and it's disputed how much of a social hierarchy really existed at the time (there is plentiful wealth in the form of gold and fine art, but no rich burials or elite residences).

As for who the Ulaidh really were, it is hard to say. Today Ulaidh is anglicized as Ulster, one of the four or five historical 'provinces' of Ireland. In the early historic period, however, they were treated as an ancient population (rather than a region) ancestral to a number of northeastern Gaelic dynasties, each claiming to be the 'true' Ulaidh. Epics like the Tain presented them as a great pre-Christian kingdom with their 'capital' at Emain Macha near modern Armagh, but this image is basically mythological. Interestingly, Emain Macha was one of the most active ritual sites in Ireland during the Iron Age. From about 400 BC the earlier Bronze Age complex underwent major modifiations, culimating in some sort of ritual about 95 BC (radiocarbon dated) in which a massive circular structure was built within an enclosure, filled with a stone cairn, burned and buried. There is also evidence on the site of foreign contacts in the form of a barbary ape skull, as well as skilled craftsmen producing works like the Loughnashade trumpet. The northern midlands around Emain Macha appear to have been the most economically active part of the country, with the majority of La Tene art and earthworks being found there and the distribution of rotary querns implying a higher degree of agricultural development.

So, even though it's pretty much impossible to say anything certain about Ireland politically at the time, considering Ptolemy's early reference to the Woluntioi and the archaeological evidence for activity at their 'capital' of Emain Macha, it is at least plausible to imagine that the Ulaidh (or whatever population was vaguely remembered as 'the Ulaidh' by the medieval Irish) existed as a distinct group in the Hellenic period and were among Ireland's most important 'tribes' or groups of tribes. But whether we're talking about some kind of powerful chiefdom/proto-state, or just a sort of regional identity shared by a group tribes or clans, is still quite up in the air.

Sources:

Philip Freeman (2001), Ireland and the Classical World.

John Waddel (1998), The Prehistoric Archaeology of Ireland.

Brian Dolan (2014), Beyond Elites: Reassessing Irish Iron Age Society, Oxford Journal of Archaeology, Vo. 33, No. 4.