I see a lot of the stories in Dwarf Fortress arising from fortuitous arrangements of random events. Because so much of the game arises from procedural, unplanned interactions, coherent or interesting stories thus have an additional aspect of authenticity. Because of this, it's not really wise to go into Dwarf Fortress looking for it to recreate the stories you imagine.
Therefore, the best way to generate stories is simply to look with imagination at events as they take place in a fortress, to read into the tiny actions of dwarves, like the fact that one of my traders likes to hang out on a lonely outcropping overlooking the city (imagine his thoughts or his reasoning for hating the others), or to look into the interactions between creatures, like the fact that my first engraver, who was killed by goblins before she did more than engrave the dining room, had one son, whose children each became mayor in their turn before succumbing to madness, and among whose children was born a girl with a score of 100 under the Artistic trait, who became the fort's next engraver.
As for influencing and adding flavor to stories, information/manipulating utilities like Dwarf Companion and Dtil/Tweak spring to mind, the former allowing you to both alter dwarves and look at the stats of enemy units (for example, turned out the legendary crossboworc who killed my entire group of marksdwarves was once a lowly fish dissector, but had gained so many levels in this skill that he had maxed out all his stats), and the latter allowing you to alter landscapes (like the magma moat in Blockedlance).
Dwarf Therapist also allows you to check the traits of dwarves - that's how I found the girl with maximum artistic propensity.
You can also mod the game. Take out normal wildlife and infest every biome with zombies, or fantastic beasts, or subtly mod giant eagles and desert scorpions so they are a common sight. Headshoots was defined by HolisticSpawn, and half of the beginning of Nist Akath was the Skelk...
Other things: speed increases attack and movement speed, and attack power, armor, etc can be changed with modding. You can turn invasions on and off in the init file, among other things. Life span is interesting because it changes the generational quality of dwarven life.