What sorts of gifts should I give friends with expensive tastes when I’m poor?

Don't get them stuff, get them memories.

Take them camping, or hiking or kayaking or go see something interesting or have a picnic, etc.  Introduce them to something they've never done before, or someplace they've never gone before. 

Stuff just winds up getting put in a drawer, or broken, or thrown away eventually.  But I still have fond memories of people taking me to do things from decades ago. 

Send them a card.  You shouldn't be expected to buy gifts for other people, anyway. I haven't been a gift-giver in years, and i don't expect people to buy things for me, either.  

If the person knows that you have very little money I am sure that the person will not expect very much as a gift, in fact, that person might only expect to receive a card so why not make one yourself. Take a little time in doing so, use a card of her favourite colour and just give her the card on her birthday. There will be no need of any explanation.  If she's a decent person she'll appreciate the fact that you actually remembered her birthday in the first place.

Many years ago I gave a man, with whom I worked, a hand made card (because I make many of them and sell them to raise money for charity).  He opened all the cards from work colleagues and, after opening mine, he looked at it in disgust and said "Oh, home-made!"  I noticed that he looked at the back of all the others from colleagues - some of which still displayed the price. On that day I vowed I would never acknowledge his birthday again.

Anyone who is not grateful to receive whatever they are given do not deserve to receive other things from those people ever again. Don't follow the crowd - ever.  There should never be a need to do that.  We are all individuals. 

Your time......

First of all, ignore "anna"s advice below. It's truly ridiculous. Secondly, instead of buying them a gift that they probably don't need, take them out to a nice dinner. It won't cost too much, and it will be meaningful to them that you want to spend private time with them celebrating their birthday. Don't take them on their actual birthday, but a few days after.

a basket of nice cheap things that look expensive and more volume looks like you spent more money 

Something useful, simple and unique. Something they'd enjoy, but wouldn't think of to buy for themselves... like an unusual liqueur or a confectionery treat for a foreign country. Those can be had for >$10.

😄

You dont.

You save your money and survive.

The best possible thing to do is give best wishes and congrats.

Then dont show up to the party to avoid being labeled a moocher.