1. Not only will I keep from littering and spitting anywhere, I will also help clean up the roadside litter whenever possible. CORRECT

2. Not only I will keep from littering and spitting anywhere, I will also help clean up the roadside litter whenever possible. NEVER CORRECT

The tricky part of your question depends on the "inversion" of the sentences Subject and Verb.

Inversion happens when we reverse (invert) the normal word order of a structure, most commonly the subject-verb word order.

We invert the Subject and Verb:

- to make questions

- when we use negative adverbs (never, seldom, rarely, scarcely, hardly)

- when we use 'here' and 'there'

- when we begin a sentence with 'not'

We invert the subject and verb after not + a prepositional phrase or a clause in initial position:

- Not for a moment did I think I would be offered the job, so I was amazed when I got it.

- Not till I got home did I realise my wallet was missing.

Here is a nice explanation:  http://dictionary.cambridge.org/grammar/british-grammar/inversion

Number one is almost correct.  "Not only will I keep from littering and spitting anywhere, but I will also help clean up the roadside litter whenever possible. 

The correlative conjunction is not only... but also.  Others are neither... nor, both... and, either...or.  They require parallelism within the structure.  Contact me if you have any other questions about this.