If you’ve ever had to do the laundry, wash the dishes, make the meals, change the bedding, vacuum the house, and clean the bathrooms day after day, you’ve experienced drudgery. Drudgery is hard, mindless, backbreaking work.
When you say the word drudgery, you can almost feel the hard, plodding work that it describes. You have to put some effort into saying the dr- sound. Then, as soon as you get through the breathy -u-, you’ve got two more hard sounds in -dg- and -er- before you get another break with the final vowel sound. Just as you might drag yourself doing those repetitive, grinding chores, you have to drag your way through pronouncing the word.