I understand your paranoia because I have this feeling when I buy carrier oils. I don't know how long these oils may have been sitting before they're shipped out. Most do have a 'best if used by' date but you never know...
Do you know who the manufacturers are for the EOs? I wouldn't be too concerned as long as they're a reputable company. This is just my opinion but I think the EOs will be fine as long as the bottles are sealed. It's really once you open them that the countdown begins on shelf life. You might find this
article from aromaweb helpful and you'll also find a link in it to storing essential oils.
Now I have a confession to make - my EOs are old, really old, a couple of years older than I've read is recommended. However, they're all in amber bottles and stored in a room that never really has much of a temperature fluctuation. (I have a theory this is because this room is in the center of the house and the other rooms act like insulators. But I'm probably just being silly thinking this is the explanation.) Anyway, they're all still good - even the citrus ones which I find amazing. Perhaps it's because I open them, remove what I need and then cap them right away. I don't know but they've lasted but I'm starting to feel I really need to finish off the orange EO. However, just because I think they still smell good and look good doesn't necessarily mean someone else would agree about their quality. My understanding is that older EOs are not considered potent for aromatherapy. I don't mind because I use them for scent and not for therapeutic qualities.
I want to mention that I'm not an expert on EOs and everything I've written is just my opinion based on what I've experienced. I'm certain experts and aromatherapists would disagree with my opinion about how long EOs really last. So, take my info with a grain of salt.
I'd follow My Mountain Soaps' advice and watch to see if any EOs change in color or smell a bit off. Also, watch for cloudiness in them.
I know Lindy is an aromatherapist so maybe she'll see this post and be able to give more information.