The average settlement in the last round of UK cases was, according to the BPI, around £2,000. At the high end, two defendants paid over £4,000 each to settle their cases. The numbers of file involved varied from several hundred to several thousand, with the higher settlements presumably reflecting more files being shared.
In the US, settlements have on average been much the same, but in some cases have been much higher. In the first wave of litigation in 2003, it seems that the average settlement was about $3,000, with settlement demands starting at about $3,000-$4,000. Individual settlements, however, included several of $7,500, and at least one for $10,000. Since then there have been reports that the average settlement has gone up to $4,000. There have also been some unusual cases involving student filesharing networks where the settlements have come in at $12,000-$17,000.
Significantly, several of the US cases have involved people who arguably weren't guilty of any wrongdoing, but who nevertheless found it safer and cheaper to pay up. Leaving legal fees aside for the moment, the main reason for this is the draconian statutory damages US law provides for copyright infringement. Instead of requiring proof of actual damage, US law allows plaintiffs to recover $750 to $30,000 per copyrighted work, which can be increased to $150,000 for willful infringement. So, if you share 100 files, that's a statutory minimum of $750 x 100 = $75,000 in damages, irrespective of how often those files were in fact downloaded. Facing the risk of these (arguably unconstitutional) penalties, it's hardly surprising that the RIAA has substantial leverage over defendants.
Turning back to the Irish situation, presumably IRMA will initially be looking for settlements in line with the majority of US and UK settlements, which would put the demands in the region of €3,000-€5,000 or thereabouts. If they restrict themselves to these figures, it's unlikely to be worth a defendant's time seeking legal advice and contesting the action, particularly since a loss would involve paying that amount and more in legal fees (for both sides) alone. Factors which will influence the amount of any settlement will presumably include the number of files involved, the length of time for which the material was shared, and (possibly) any mitigating factors such as the sharing being unintentional or by a child.
If a filesharing case did go to trial, it's difficult to put a figure on what damages might be awarded (and possibly redundant, since the damages might well be dwarfed by legal fees). Irish law does not have statutory damages comparable to US law: the damages which can be awarded are generally limited to the actual loss suffered by the plaintiff (which will be difficult to prove in filesharing cases), though aggravated and exemplary damages can also be awarded in particularly serious cases. The only reported Irish decision discussing damages in this type of case seems to be Universal Studios v. Mulligan where the court awarded (in 1999 pounds) £75,000 damages to various film studios injured by the defendant's sale of several thousand pirated videos, of which £25,000 was compensatory and £50,000 aggravated. That case, though, involved a large scale commercial operation, over a period of years, which made the defendant substantial sums of money. It's very unlikely that an award of damages in a filesharing case would come anywhere near that benchmark - and judging from Universal Studios, it's also unlikely that aggravated damages would be awarded.
Update - The Register reports that eight Dutch filesharers have settled for approximately €2100 each. According to EDRI the filesharers were required to:
sign a unlimited binding agreement to never ever "directly or indirectly be involved in any way or have an interest in unlawfully distributing materials on the internet". If ever again caught in such a very broadly defined act, the signee agrees to pay a fine of 5.000 euro per day.