First off well done in recognising that the finish needs to be refreshed now, and not putting it off for longer and have the surface weather further (which isn't likely to result in damage but the looks would take a hit).
I’m unsure if I should just apply the oil or if I need to sand or pressure wash it first?
In general you do always want to at least clean a surface before you reapply finish or apply a layer of a new finish, and pressure washing is an excellent way of doing this.
The instructions for the "teak oil" you bought might not specify cleaning, or even imply it, but it's always good practice. In case it's not obvious, the wood must be left to dry thoroughly before the finish is applied.
The instructions also may or may not suggest abrading1 the surface, but even if they don't you can do this. Judging from the photos I don't think it's a requirement in this case, but since it doesn't do any harm I think it's usually a good idea to do it anyway. You're only looking to make the surface more receptive to new finish, not in any way trying to uniformly expose a fresh wood surface. Literally a couple of light passes is usually enough, all of a few minutes' work.
Brush/wipe dust off and you're ready for the finish to go on.
After application and possibly a short wait time, all instructions for finishes of this type will say something about wiping away excess but it's normal for this not to be given enough emphasis. You are seeking to wipe away ALL excess; the surface should not be noticeably oily when you're done.
Since the wood was previously finished one coat may be enough, but you may need to apply two coats to achieve uniform colouring and surface sheen. Be guided by what you see.
Safety note: if you use cloths or paper towels for application or removal of excess oil these are a fire hazard and these can spontaneously combust in the wrong conditions. But it's simple to deal with them safely, just lay them flat on the ground until they have gone stiff and you can then dispose of them as normal household waste.
Afterwards
Once dry to the touch the finish is not nearly at full strength, so only use it lightly (if at all) and avoid exposure to weather for at least a week. If possible wait a fortnight or longer.
Most "teak oil" products are fundamentally the same and here is a sampling of the instructions from a few manufacturers:
Ronseal
Liberon
Watco (note, owned by Rustoleum)
TotalBoat
As you can see the application guidelines are broadly similar but may mention something that another does not, so look for a detail like this for the product you've bought.
1 Almost always sanding will be specifed but this doesn't mean you have to use sandpaper, you're just looking to lightly abrade the surface. This can be done with any med-fine abrasive paper, cloth or screen (180-240 grit is about right), or with Scotch-Brite or another non-woven nylon abrasive — you can use a nylon scouring pad in place of something specifically marketed for woodworking.
