The words effect, impact and influence can be used as nouns or verbs.
To effect (verb) means to bring about a result, which is an effect (noun).
a) The new rules will effect (verb) a needed change.
b) The new rules created the needed effect (noun).
In the above examples, you could have said:
a) The new rules will CREATE a needed change.
b) The new rules created the needed RESULT.
To influence (verb) is to effect in a more subtle, partial, less complete, softer way than "to effect". Examples:
a) The color you wear will influence (verb) what dress I decide to wear.
b) The color you wear will have an influence (noun) on what I dress decide to wear.
In the above examples, it is implied that "the color you wear" is an influence on, or one factor in, my decision, but that it is not the only important factor in my decision.
You could have said:
a) The color you wear will HAVE SOME EFFECT ON what dress I decide to wear.
b) The color you wear WILL BE A CONSIDERATION IN what dress I decide to wear.
c) The color you wear will BE ONE OF MULTIPLE FACTORS IN what dress I decide to wear.
Impact is a word which, as both noun and verb, now has two common definitions; the second definition is a result of past misuse of the first definition. The second definition is now common use and, to the best of my knowledge, acceptable in all forms of communication.
To impact (verb) means to strike, to collide.
An impact (noun) is a collision.
To impact (verb) means to have a powerful, immediate effect or influence on.
An impact (noun) is a strong, immediate effect.
Examples (of second definition):
a) His speech will impact (verb) the election results.
b) His speech will have an impact (noun) on the election results.
In both above examples, "strongly effect" (verb) or "strong effect" (noun) could have been substituted for "impact".
"Affect" is an often misused word related to the above.
To affect (verb) is essentially synonymous with "to influence".
Do you think the weather will affect how many people come to the party?
However -- "an affect" (noun) is NOT related to the above and can NEVER be used in place of effect, impact or influence. An "affect" (noun) is a technical term for a mental state used in medicine and psychology.
Hope that helps. rebecca