Cfrtjryk

I want to say something like: from now on I will work on my second task.

Is it correct to use "onward" (just onward) at the beginning of the sentence to replace "from now on"?

Onward, I will work on my second task.

Onward sounds odd and is uncommon at the start of a sentence.

Here's the definition of onward in the Oxford English Dictionary, adverb, entry 4b.

In an uninterrupted advance or succession forward in time. Cf. on adv. 4a.

The definition of on referred to is the same on used in the adverbial phrase "from now on." So the two have some relation to one another.

My issue with your example is that "onward" isn't an adverb commonly used at the beginning of a sentence to modify that entire sentence. In the Corpus of Contemporary American English, it appears at the beginning of the sentence in a different sense: proceeding forward in space to a destination. "Onward!" appears. "Onward to [some goal]" appears. "Onward [people being urged forward]" appears. No start-of-sentence "Onward, I ..." formation appears. The closest that appears is "from that moment onward, I ..." That last usage highlights that, when "onward" is used in a temporal sense as an adverb at the start of a sentence, it tends to be incorporated into an adverbial phrase that gives more context. So in usage, onward at the start of a sentence usually comes with some extra information: from what or to what?

Given that evidence, I would use "from now on" if I wanted to be perceived as correct and "onward" only if I had some deliberate purpose in mind.

No, the cited usage is not idiomatic. You need something like From now onwards, I will do that.

If you compare AmE and BrE corpuses on that link, you'll see that both massively favour onwards over onward in that exact context - which I found interesting, given that AmE always favours toward over towards (with Brits it's the other way around).

A bit more sniffing around showed me that Brits are about equally divided over whether to include the s or not in a "phrasal verb" context such as to move onward / onwards - but in that context, Americans much more definitely prefer to move onward.

So regardless of what you read about the "standard" US/UK distinction (telling us that the "s-less" versions toward, upward, downward, onward are used in AmE, whereas towards, upwards, downwards, onwards are "British"), this doesn't seem to be true for OP's exact context (from now / then onwards).

Is it correct to use "onward" (just onward) at the beginning of the sentence to replace "from now on"?

Onward, I will work on my second task.

Yes, it is grammatically correct, as is the more used onwards.