All of your sentences are grammatically correct, yet they leave plenty of room for stylistic improvement. For good style, using good grammar is important, but not enough. Let's talk style.
Your version with a period, if the need for rephrasing is disregarded, is fine, though you could have used a semicolon, too. "Either approach is permissible."
On to rephrasing. It doesn't stand to reason to separate pants, handkerchiefs etc. from shirts and sweaters, for all of those articles of clothing are equally susceptible to, as you put it, "the most terrible stains." Rust and ink don't discriminate jackets from shirts. I infer that what actually prompted you to divide your thought via a correlative conjunction was the distinction between the capability to "effectively wash" — which phrase features a marketing-friendly adverb, but actually refers to common, everyday cleaning of moderately soiled laundry — and the capability of special, price-tag-justified cleaning of the most stubborn stains. You should always strive to structure a sentence so it reflects how you mentally have categorized the information. That implies that during the writing process, you need to consciously inspect your mind. So, let's try to put apples with the apples and oranges with the oranges.
This powder is able not only to effectively wash but also to clean out the most terrible stains on your shirts, sweaters, pants, handkerchiefs, socks, jackets, shawls, veils and most other kinds of clothes.
Note that when the subject of a sentence is not among the things correlated (above, the predicate is correlated), the comma before but also is unnecessary. OK, but our work is not even close to being done. Of utmost importance: wash now, unexpectedly, governs stains, not the articles of clothing. Let's not have wash govern anything; let us change it into a noun. Secondly, let us further meaningfully sort out the types of cleaning. Thirdly, although clean out and terrible are informal expressions, kinds of clothes sounds a bit too informal. Therefore:
This powder is not only effective for daily washing but can also clean out the most terrible stains on your shirts, sweaters, pants, handkerchiefs, socks, jackets, shawls, veils and most other articles of clothing.
Lastly, with correlative conjunctions one should always attempt to keep the correlated grammatical parts of sentence identical. But, not at the price of fluidity. A persnickety fussbudget, though, would require total syntactic parallelism, and the sentence would then be rendered as:
This powder not only is effective for daily washing but also can clean out the most terrible stains on your shirts, sweaters, pants, handkerchiefs, socks, jackets, shawls, veils and most other articles of clothing.