The principle of Peak Oil still exists, as it must with any finite resource. But how and when will the peak occur, and is that still relevant?
Peak oil is an issue of price vs. cost vs. supply/availability vs. demand vs. alternatives. Each of these is influenced by (geo)political scenarios of which there are many, most are influenced by eachother, and a few big issues have also raised their heads (see point 6).
Your questions regarding EOR and Shale gas are, as Sacha indicated, related to oil price. Shale is rarely an economical option under $50 and if EOR can be done cheaper it may be preferred. So EOR applications on the high end are unlikely to be worthwhile.
Back to Peak Oil: 1-price, 2-cost, 3-supply, 4-demand, 5-alternatives and 6-COP21.
1) Price: a large part of oil price is speculative value (various analysts estimate 30%-50%), and both geo-politics and local politics (i.e. financial regulation) influence this. There are many views on price, but over the last 25 years the "value estimate" was typically from $20 to $50, rarely higher.
2) Cost can be reduced, but in my opinion (in shale gas, but to some extent in EOR also) this is now largely against risk rather than efficiency. So if risk can be externalised (i.e. regulations adapted to remove industry liability) cost can drop, otherwise this may be difficult. Lowest cost is linked to region, and my region for instance (North Sea) has little hope.
3) Supply is closely related to cost. At $200/bbl our hydrocarbon reserves are huge, enough for wholesale planet destruction if it's all burned, while at $10/bbl many regions fall by the wayside. Most shale and EOR efforts follow abnormally high prices, supplying reserves we can't use now.
4) Demand changes. Economic cycles impact it, but e.g. inefficiency accounts for ~40% of global energy use: more efficient customers can change the picture radically, often at a cost less than the cost of oil. But availability of alternatives and environmental regulation will also influence demand, and once alternatives become price equivalent and reputationally preferred, Peak Oil has arrived.
5) Alternatives are now often cost-competitive with hydrocarbon, and will become more so. They are becoming "volume competitive", often have the margin on security of supply, and they're just beginning.
6) How about Climate Change? With COP21 going on in Paris we can't ignore the fact that the world will be reducing its emissions and this will mean reducing hydrocarbon use, down to zero emissions (not quite zero use) in 35 to 85 years. (CCS can never do more than assist on a small scale)
Peak oil is here, and the dropping cost of viable alternatives will keep it here.
Much of this data can be found in my Devex poster of March 2015.