Hi Mike!
Good questions!
I haven’t actually spent a lot of time studying this correlation issue and petrocurrencies, but I am sure that oil prices do indeed have a range of effects on practically all economies and currencies in various ways and to various extents!
I guess the two main reasons for this are that a) oil is almost always priced in US dollars (or nowadays Euros, too), which means there is usually some kind of large-scale foreign exchange transactions involved in oil deals, and b) oil demand for most countries is both large, critically important and relatively inelastic (at least in the near term) regardless of oil price changes.
The most obvious impacts are on the major oil exporting countries and oil importing countries since the size of the oil industries in these countries is always significant - and especially when oil exports/imports are a high percentage of total exports/imports. An increase in oil prices will create an increased inflow of currency to oil producers which, when exchanged into the domestic currency will create an upwards pressure on it. Similarly, importing countries have to pay more US dollars for their oil and therefore sell more domestic currency to do so.
Apart from this direct impact of foreign exchange through the oil transactions themselves, there is also a general boost from oil price rises to the economies of producer countries in the form of extra tax revenues, employment, additional investment programmes, overflow into related sub-contractors and service industries, etc.
But I guess there is also a contra effect as well in that when a domestic currency strengthens it will also increase the price of exports to other countries and will reduce competitivity.
However…
Having said all that, I do not think that the correlation between oil prices and currencies is realistic enough to use as a basis for trading decisions - at least not on our kind of time frames. Oil is only one factor affecting any particular country and there are, of course, many more factors that will have a greater or lesser impact at any given time.
By way of example, as you mention, one currency pair that should clearly show this correlation would be CADJPY since Canada is a significant oil producer and exporter whereas Japan is a big importer. So I thought I would put up a daily chart for each of these side by side. Here it is, since Jan this year, with USOil on the left and CADJPY on the right. Unless I have done something very wrong here, I don’t see any correlation at all!
In the meantime, May Day is a big celebration and public holiday here, and since it has been a brilliantly hot and sunny day, we’ve been more concerned with a hike in the forest and grilling sausages - even if the lakes are still frozen and the last remnants of the winter’s snow still stubbornly visible