I know
@Smurf1976 probably has something interesting to add.
Ultimately the end uses of energy can be divided into a few key categories:
Electricity
Transport
Industry
Commercial
Residential
Note there that "industry" or "residential" means the direct use of fuels in factories or homes and does not include their use of electricity.
Now looking at those the reality is that there's considerable short term flexibility in the electricity and industrial sector to switch between fuels based on price. In the long term that also applies to the commercial and residential sector when equipment wears out and is replaced etc. It's really only the transport sector which is really stuck - can't run a plane on coal for example.
LNG projects are capital intensive when compared to oil in that it's not just producing the resource but the liquefaction, shipping, storage and regasification is all rather expensive when compared to the comparatively cheap and low tech process of storing oil in a simple tank at ambient temperature and pressure. Oil's a lot easier to handle than gas and has no need for all that costly infrastructure.
LNG contracts are thus commonly set with reference to the oil price since an electricity utility, and they are the largest LNG buyers, isn't going to spend all that money on infrastructure without some assurance that they're actually going to get cheaper fuel by doing so.
So for contract LNG it's commonly set with reference to oil as a benchmark. For spots sales well they're still competing with other fuels especially oil.
A lot of industrial boilers, power generation etc can switch between fuels seamlessly. That is, they can do it without even a drop in output during the change, production continues completely uninterrupted. As such they will go for whatever's cheapest - that's gas under normal circumstances but if it wasn't then they'd be switching to oil real quick.
Not all power generation or industry has that capability but enough does to create a situation where the ability to substitute one for the other is significant in practice.
A key factor with gas is that it's a local commodity as such rather than a global one. If there's no or very limited ability to import / export from a gas system then the local price won't reflect any international price for example. The USA is the most obvious example there - exports aren't zero but capacity is very limited and the domestic price has in recent years remained below the international prices for that reason.
So looking at market pricing of the various things which "oil" companies listed on the ASX produce:
Crude oil = self-explanatory and it's directly tied to the oil price.
Condensate = this is a by-product of gas production which is sold to oil refineries as feedstock for the production of petrol etc. It is counted as "oil" for statistical purposes globally and its price also follows the oil price despite its association with gas. Anything referring to total oil reserves etc will commonly refer to "crude + condensate" for this reason. Consider it to be oil in practice for financial purposes.
LPG (propane and butane) are a gas at ambient temperature and pressure but the hint's in the name - Liquefied
Petroleum Gas and that's exactly what it is. LPG is not LNG, it is not natural gas, and LPG is closely tied to oil in terms of most end uses and price. Some LPG is also produced at oil refineries. So whilst it doesn't always strictly track the oil price and is not oil as such, it mostly does and most publishers of statistics, either government or private, do include LPG as "oil" for that reason.
Ethane is a minor component of natural gas. It's either stripped out and sold separately (as a gas not a liquid) to petrochemical producers or in small amounts it's left in the natural gas supply to consumers if there's no local petrochemical producer wanting it. In a few cases it is used as fuel in its pure form at specific facilities. Financially it's not a major market in most parts of the world - it tends to be either sold as though it were natural gas or sold under contract to a specific end user.
Natural gas (methane) or LNG is as per the name. Comments as above about its linkage to the oil price.
Electricity - OP mentioned Origin and they do generate electricity, the market price of which is its own market although fuel costs are a key influence.
Retail - Origin is also a retailer of gas and electricity to consumers as well as a physical distributor and retailer of LPG. These markets and the profit derived from them don't have a lot to do with the underlying commodity prices since it's the retail margin that's of significance. Companies involved in this area often venture into other retailing as well - most common example is selling internet services but there's also a few who've tried selling house insurance and other things totally unrelated to energy. They're simply a retailer in that role, a middleman basically.
Bottom line is that the Australian gas producers are "substantially" exposed to the oil price apart from any hedging etc they've entered into. Not fully but substantially and with Origin being less exposed than the rest due to its power generation and retailing operations which form a substantial part of the business.
Even those who don't themselves produce LNG, they only sell gas domestically, are still selling into a market where price is heavily influenced by what the LNG producers are willing to pay for gas. As the oil price has come down, we've likewise seen gas prices drop in the Australian domestic market indeed for the east coast they're down more than half from where they were a year or so ago.
That is also putting downward pressure on electricity prices at the wholesale level in most states. Comparing 2018-19 financial year with 2019-20 year to date:
Queensland = $94.41 / MWh last year, $72.53 so far this year
NSW = $97.93 / $84.32
Victoria = $119.02 / $97.27
Tasmania = $90.65 / $60.68
SA = $126.12 / $82.90
There are other factors also but the drop in the gas price is definitely a contributing aspect. Whilst most electricity does not come from gas in Australia, for the above states collectively it's in the 8 - 9 % range over the year, reality is that if you're generating from coal or solar or whatever and want to maintain volume well then you need to under cut gas or oil otherwise you'll be pushed out of the market on price alone. The lower the gas price goes, the lower your price for power from coal or hydro needs to be if you want to stay in business. Etc. Only time that doesn't apply is when demand's high to the point that everything has to run - that happens but not constantly.
There's also an international aspect there. The electricity companies generally don't say much publicly but there are some which do in practice have exposure to international prices in regard to contracts for supply within Australia.
Australian domestic (east coast) gas pricing has been running around the $5 - $6 per GJ mark in recent weeks, equivalent to oil at AUD $30 - $36, but it's pushing to the bottom end of that range now. Gas will under normal circumstances always be at a discount to oil unless there's some very definite scarcity issue etc in a particular region.