The 'hue' refers to the hue and cry, it means starting the hunt to find the killer. In fourteenth century Essex this was normally begun by notifying your four nearest neighbours. They would then tell the bailiff of the hundred (a division of a county), who would then inform the coroner. It was the duty of the first person to discover a death to raise the hue and cry.

The inquest was actually carried out before the coroner by jurors from the four neighbouring towns. In medieval English law jurors did not hear evidence and then decide the outcome of a case, as they do today, instead they presented evidence and an official, in this case the coroner, would make a ruling based on their testimonies. Jurors were normally local people knowledgeable about the case. So what happened here was the coroner summoned a selection of people from these four villages and asked them to present any evidence they had about the death, but they claimed to know nothing more than the initial report.

Pledges were people who provided sureties for someone involved in a case. For example, someone could become a pledge to ensure that the defendant would answer the case, or that the defendant would pay the fine or debt the court assigned to them. To act as pledge could be risky, you could be fined if the person you had pledged for did not appear in court and if they failed to pay the fine they owed the court, then you could be fined too. However, it seems that most took the risk. A study of one Worcestershire village found that the average man recorded in the court rolls became a pledge around sixteen times.

The dating system you refer to is very common in medieval documents. Rather than being dated the way we might today, e.g. 12th July 1345, medieval documents could use a range of references to refer to a particular day. For example, a coroner roll might be dated something like this: Sunday after the feast of St Luke, 28th year of King Edward son of King Henry. To work out this date you'd need a copy of Cheney's Handbook of Dates (see the source list below). It's invaluable for working with medieval primary sources.

All of the lists and tables used in the following are found in Cheney. To calculate the date you would first need to determine the year. The reference here is to the 28th regnal year of Edward I. He became king on the 20th November 1272, and so his regnal year begins on the 20th November and ends the 19th November. Therefore his 28th regnal year was 20th November 1299 - 19th November 1300. Now we need to work out the date of the feast of St Luke, which was the 18th October, so the year must have been 1300, towards the end of Edward's 28th regnal year. The next thing to work out is the day. This is done by calculating when Easter was that year. Cheney gives the date of Easter in 1300 as the 10th April. Looking at his calendar for that Easter date, the Sunday after St Luke was the 16th October. So, from this we can translate the medieval date, Sunday after the feast of St Luke, 28th year of King Edward son of King Henry, to mean 16th October 1300.

There may be other terms in the dating that you come across as well, such as vigils and octaves. If a day is described as the octave of a feast, then it means the date is eight days after the feast (counting inclusively), so the octave of St Luke is the 20th October. The vigil is the night before, making the vigil of St Luke the 12th October.

Sources:

C. R. Cheney, A Handbook of Dates for Students of British History (Cambridge, rev. ed., 2000).

R. F. Hunniset, The Medieval Coroner (Cambridge, 1961).

Zvi Razi, 'Family, Land and the Village Community in Later Medieval England', in T. H. Aston (ed.), Landlords, Peasants and Politics in Medieval England (Cambridge, 1987), pp. 360-393.