There are several questions here...
By winning this can they [Brexit Party] have a significant impact on Brexit?
No, in that they're not in power; but also yes, because they won the EU election in the UK. In the process, unhappy Tory voters have sent a rather clear message to their MPs that they'd like them to get on with Brexit and move on to other things. (But see below.)
If they do why UKIP, didn’t have such an impact for last 3 years on Brexit?
Farage left UKIP after the Brexit referendum, and the party has become a weird extreme right outfit that lost its soul when it began to accept racists like Tommy Robinson amongst its senior leadership.
After winning the election, Brexit Party leader Nigel Farage said the victory sends a strong message to UK politicians.
Except for the fact that, when you combine the votes of clear-cut Remain and Leave parties, and agree with the notion that this was the de facto referendum, well... Remain wins. If you fold Tory votes into Brexit and Labour votes into Remain (a dubious idea in both cases IMO, but it's probably a good enough approximation), the result is even more clearcut: the UK wants to Remain. So the message is very strong indeed. But for Remain.
As the UK is leaving the European Union soon and assuming the Brexit party doesn’t have a significant impact on the Brexit deal (or no deal) in either the UK Parliament or the European parliament, what is the victory here?
It's not at all clear that the UK is leaving the EU anytime soon. The victory is that they humiliated the Tories (as in "get on with it", basically) and came in a strong lead in the EU elections.
What is going to change between now and October?
Not much in all likelihood. There's going to be a new PM, and that's the only thing that's certain.
There already are signals by senior Tories that a PM who would pursue a no-deal Brexit will get kicked out of office. And the EU has made it crystal clear that it's this deal, period -- and the UK isn't in a position to renegotiate. So assuming new snap elections don't occur it's going to be about whether a new PM will be able to (finally?) sell the current deal to Parliament and/or the public, or convince the nation as a whole that actually, Brexit isn't going to happen. Or just kick the can down the road.
If snap elections do occur it's really anyone's guess. FWIW mine would be that the UK would end up with an election entirely focused on Brexit and it would turn into a wholesale referendum (again). And I'd stick my neck out and suggest that either Article 50 would end up revoked in such a scenario, or the resulting Brexit deal would be so soft that it would make Brexiters even angrier.
Side note on the latter point: May's deal is the hardest possible Brexit deal based on the redlines she gave the EU and what the EU is willing to accept without putting itself in jeopardy. IMO there is just no way a new PM will get a better deal, and the EU has also made very clear that even in the event of a no-deal Brexit a prerequisite to even beginning to negotiate a future trade relationship is to accept what's in the Brexit deal -- including the controversial backstop.
And what’s the strong message this result sends to U.K. politics?
Purportedly the message is that there's a strong block behind a no deal Brexit. But as we've seen above, it's only purportedly. In reality, there's a strong block behind no Brexit. So this is just spin.
