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I bought the oak dowels supplied as 25mm x 300mm to fix through three oak sleepers total height 300mm.
I then bought a 25mm auger bit.
When I just checked the dowels with a calibrated digital caliper, the diameter came up as 25.4mm. Is that normal? Would I be able to hammer them in a 25mm diameter hole?
On a small scale wood is highly compressible, so the basic answer here is yes. As a joke goes, you might just need a bigger hammer ^_^
Is that normal?
Yes it's quite normal for shop-bought dowel to measure slightly off its nominal size.
In fact it might be accurate to say that dowel is rarely the stated diameter. It can be larger or smaller. Occasionally you'll even see dowel for sale that has already gone slightly ovoid — so, over dimension in one axis, and under dimension at right angles to this. Although this generally takes some time to happen (more than a few seasons) stock turnaround might be low enough that you'll see it on 'new' material.
Would I be able to hammer them in a 25mm diameter hole?
The basic answer is yes as stated at the outset. However, a further surprise might be in wait for you when you check the auger. Even drill bits are frequently not exactly the size stated!
If the auger does happen to measure as exactly 25mm, do note that drilled holes are always larger than the bit that made them. This is true even in hard materials like steel (!) and even when made in a very rigid setup like on a drill press/bench drill.
So, assuming your bit did happen to be exactly 25mm, the thing you think you're facing — hammering in a dowel to an undersize hole — won't actually be an issue.
Regardless of the exact fit, you do need to drive the dowel very deeply here, much deeper than would be commonly needed. And if the fit is tight the friction will get higher and higher the deeper you pound the dowel in. It is possible that you will even get to the point that you won't be able to drive the dowel in any further.
Glue?
If you intend to glue, note that some glues increase friction and others do not.
Foaming poly and epoxy are highly lubricative and don't produce 'grab'. They're also reliably 100% waterproof, which argues in their favour anyway.
PVA on the other hand can massively increase the friction, due in part to its high water content, and as a result could easily result in the dowel becoming impossible to insert further once in a certain depth.
No glue
If the plan is not to use glue, you can increase your chances of success by lubricating the dowel. You can do this with wax or oil.
