Storing a finished cake

It is the customers problem.  Have them pick it up as scheduled.  I would suggest they freeze it but there probably be a problem with the fresh strawberry layer.  You certainly can do it as a do-over if they pay you for the second cake made fresh for next week.  Their  change in plans is not your problem, don't let them make it yours.
 

My best answer is No, the cake needs to be paid for and eaten (or chucked ).

It won't hold up for a week (and no one should be eating a week old cake [stored at room temp OR refrigerated] that contains fresh berries).

You can try freezing it, but my guess is that the tier with the fresh berries will be mush (berries have a lot of water in them, water expands when it freezes--this ruptures the cell walls, and then there's nothing to hold in the liquid when they defrost, so it's like they become a layer of juice, not berries).  I would expect this to compromise the structure of the bottom tier and perhaps even the stability of the stacked cake.  I, personally, wouldn't agree to do it.

I'd tell the client to pay for it, take it, and enjoy it or give it away.  They can re-order it for next weekend--if you're able to do it.  If they say no, then you get to dispose of the cake in whatever way you want and she gets no future cakes. 

If she had ordered flowers, she'd have to pay for them and order more--they wouldn't keep for a week.

If she'd ordered prime rib dinners, she'd have to pay for them and order more--they wouldn't keep for a week.

Actually, she can change her party date to any day she pleases--next year, for that matter--but if she does it so late in the game, SHE HAS TO ACCEPT THE CONSEQUENCES OF HER DECISION--in this case, having to pay for the completed cake AND pay for it's replacement.

If you freeze it, box it, wrap the box in 2 layers of saran wrap and a layer of foil.  24 hrs. before delivery place wrapped box in fridge, 4-6 hrs. before serving, place wrapped box on counter to come to room temp.  Right before display, remove box. 

Make the client sign a waiver--after having paid in full, of course--stating that she understands the risks and possible problems and that she waives any right to claims for appearance, texture, flavor, or stability.  The sale is final.  No refunds.  No complaints on the internet, etc.

Rae