Irksome comes from Middle English "irk" (meaning weary, troublesome) plus the suffix "-some", (from Old English -sum) meaning "tending to", "apt to" or "causing".  It appeared in the early 15th century and was derived from older roots possibly linking to Old Norse "yrkja" (to work) or even Celtic for "harm", meaning something bothersome or tedious.  It may also stem from Old English weorcsum ("painful" or "hurtful").  It describes things that cause annoyance, weariness, or vexation through repetition or persistence, like an "irksome task" or "irksome restrictions".  In essence, an "irksome" thing is one that makes you feel weary or bothered, much like tiresome work or annoying repetition. 

According to the Oxford English Dictionary (OED), the adjective "irksome" first appeared in English during the Middle English period (1150-1500), with the earliest recorded use found in 1435, in a translation by Richard Misyn, bishop of Dromore. 

Examples of "irksome" in a sentence: 
"It is irksome that some common sense preventative measures are not in place." 
"Why subject yourself to an irksome book when so many sublime ones are available?" 
"More than 1,700 passengers were surveyed, returning the five habits cruisers find most irksome."
"The restriction on upward mobility is becoming increasingly irksome to young, highly qualified, and knowledge people." 
"He found the slowness of criminal trials particularly irksome and his attempts to speed them up did not find favor with the Bar." 
"It's particularly irksome when you are designing a house and have to explain yourself explicitly to your builders for the sake of clarity." 

Just the facts:

IRKSOME Definition & Meaning - Merriam-Webster

IRKSOME Synonyms: 59 Similar and Opposite Words | Merriam-Webster Thesaurus