There are 2 broad strategies in Abandon All Artichokes: remove all artichokes from your deck, or have such a large deck that you have good odds of drawing a hand with no artichokes.

Good early game cards:

• Carrot - composts 2 artichokes, with no opportunity cost since you have no other cards to play
• Potato - good odds of finding an artichoke to compost in the first rounds
• Broccoli - likely to have at least 3 artichokes in hand
• Eggplant - compost an artichoke, though the passing probably won't have an effect
• Beet - random card from hand is almost certainly an artichoke to be traded or composted

Good late game cards:

• Leek - steal non-artichokes from opponents
• Eggplant - if you have at least 3 artichokes in hand, lets you compost one and pass the other two. If you're lucky, they might not have enough artichokes in hand to pass you 2
• Pepper - stack your deck so you're more likely to draw non-artichokes. Can also put an artichoke there for Potato to compost
• Beet - play the Beet when you only have artichokes left in your hand so the artichoke is randomly selected for trade/compost. Maybe you'll get something useful from an opponent!

Good no artichokes strategy cards:

• Carrot - compost 2 artichokes
• Onion - compost an artichoke
• Eggplant - compost an artichoke

Good big deck strategy cards:

• Corn - get extra cards into your deck. Disadvantage: have to hold on to an artichoke to play
• Peas - get extra cards into your deck: Disadvantage: gives to your opponents
• Pepper - stack your deck so you're more likely to draw non-artichokes

Opportunities:

• Opponent has no deck or discards - if opponent has 5 cards or fewer, play Onion or Peas and give them a card, then play Leek to take it right back (and play it yourself)
• Corn + Pepper + Potato - to guarantee success for a Potato, play Corn to put a fresh artichoke in the discards, then play Pepper to put that artichoke on top of the deck.