Answer: It's going to be difficult to eradicate the weeds while still maintaining the blueberry plants. Hand digging and pulling out the roots of the weeds is the first step. Covering the area with black plastic will stop the plants from growing (they need sunlight). If you have the patience, you can cut the tops off of the individual poison ivy and honeysuckle stems and then paint the stubs with a vegetation killer such as Round Up. Round Up is a contact herbicide so you don't want to spray it anywhere near desireable plants. If you daub it onto the stubs of the weeds immediately after cutting, the herbicide will be transported back to the root systems but it won't translocate into the soil so your blueberry plants will be safe.
Best wishes with your blueberries.
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