Hi Chris,
I thought it might be useful for me to chime in here.
If pushed to translate all of the above terms, I would translate them as the following. I've given you sentences to go with each which should hopefully help:
產生 To produce/to give rise to
新時代產生了大量的新詞彙 The new era produced a large number of new words
聽了老爺在戰爭中所作的英勇事蹟,我就產生了參軍的念頭 Listening to my grandfather telling me about his heroic deeds during the war gave rise to my idea to join the army
導致 To lead to/to result in
壓力太大將導致健康惡化 Being under too much pressure will lead to deteriorating health
戰爭的爆發導致許多平民流離失所 The break out of war resulted in many normal people becoming destitute and homeless
創造 To create
只有要通過自身的努力我們才能创造更加美好的未来 Only through hard work can we create a brighter future
王先生創造了新的作品 Mr. Wang created a new work
造成 To bring about/to cause
孩子做出的蠢事給爸爸媽媽造成了許多不便 The stupid thing the child did caused a lot of hassle for his parents
今年的洪澇災害給災民造成了巨大損失 This year's flood caused/brought about large losses for those affected
You're correct in saying that these words are all fairly similar. Similar to in English, some verbs are just used more with some nouns than others. In you example sentence, 產生 can be replaced with 造成 as both can go with 影響 and the meaning would be the same.
Lastly, 產生 is probably the most flexible:
同學們之間產生矛盾要及時解決,以免影響團結 When classmates have a problem with each other, they should sort it out in a timely manner, so as to not negatively affect their unity
新老師剛來,就使孩子們產生了好感 A new teacher had just come, which made the kids curious
小明對古典文學產生了濃厚的興趣 Xiaoming became very interested in classical literature
小王的亂說的一句話,使李明產生了很深的誤會 An offhand remark Xiaowang made, made Li Ming have a very big misunderstanding (this is awkward, but I hope you get the idea)
在困難面前,不要產生畏懼情緒 When facing difficulties, don't get scared
Laurence