First, would be reactive actions from whom they fought with. In Wessex, Burhs were built in order to protect livestock, wealth, and people from Viking raids. These 'burhs' provided a sense security and kept wealth and goods in the country. Also these Burhs became the first 'real' towns in England since the Romans left and set foundation greater governance and trade.

Second area of impact was when the vikings settled they also established settlements of their own that had the same effects as anglo-saxon burhs, some of these included York, Dublin, Galway, etc etc. There positive effects would be more felt in Ireland than for England because some towns and infrastructure were left over from the Roman occupation. These viking settlements become centres of trade and economic growth. Usually this meant that they would sometimes ally themselves with local population against other viking fractions because it was in their interest. Leading to some of these places being more secure from attacks by other vikings. But more importantly though the vikings bought with them trade links from their old homeland, these links allowed trade from Galway to Constantinople.

I discussed both the positive and negative impacts of Viking rule in the late 10th century here.

Your question asks about the impact on the countries they invaded, such as England or Ireland. Since neither of those countries existed at the time, I'm not sure if you are asking about long term economic effects on the regions that would become those countries, or if you wanted to know the more immediate everyday effects on those areas. The comment I linked to does the latter.

It discusses mostly their colonies in York and East Anglia, however the Dublin settlement also experienced many of the same benefits of Viking rule.

Keep in mind that the countries that the Vikings invaded in "England" were the Saxon kingdoms of Northumbria, East Anglia, Mercia and Wessex. They also made an alliance of convenience with the Cornish, because no one hates a Saxon like a Cornishman, and they harassed but did not colonize the Welsh.

I am less familiar with their Scottish and Irish adventurism and colonization, but they were present in both of those regions as well.

Their economic impact can be said to be mixed to good, and it depends largely on what your societal role was. There's a couple of good sources in the comment, but the one that is most likely helpful for you would be:

Viking Age: Everyday life during the extraordinary era of the Norsemen - Kirsten Wolf

I hope this helps with your question about the Danelaw! Additionally the comment from /u/Del-JJ regarding the burghal reforms (driven largely by King Alfred's vision for society) were undoubtedly made possible by experiencing an actual invasion. The Vikings both altered the immediate economy and trade connections in these regions but also helped motivate some pretty groundbreaking reforms by showing the Saxon inhabitants of England that the painful reforms were necessary.