How do I delete multiple points in Illustrator?

With the lasso tool (shortcut Q) you can quickly select the anchor points you want to delete, when selected you can press the delete key to delete the anchors.

How do I get rid of unnecessary anchor points in Illustrator?

Use the Simplify Path feature in Illustrator to solve your problems related to editing complex paths. The Simplify path feature helps you remove unnecessary anchor points and generate a simplified optimal path for your complex artwork, without making any significant changes in the original path shape.