You azaleas will love to be pruned back! They'll be beautiful! It might be a bit late in the year to do it now, depending on what winters are like in your area. You don't want to encourage tender new growth too late in the year if you get a lot of hard freezes during the winter. Another thing about pruning this late is that you may sacrifice some of next year's flowers, but after that, they will bloom profusely.
When renovating an overgrown azalea or rhododendron, I usually begin by cutting the plant back by about 1/3. I make the cuts just above a leaf node, to encourage the development of the leaf buds there. That will give you a nice, full, bushy shrub. If you need to cut them back more than 1/3, I would wait until immediately after the shrub flowers next year, and then prune it back by another 1/3. Just keep working at it, until the plants are the size you want them to be.
I feed mine once in the very early spring, before flowering, and again immediately after they've finished flowering. I've been told never to feed them after July, however, because it will encourage new growth too late in the year.
Get the honeysuckle vine out of the azaleas. Be aware that azaleas and rhododendrons have very
shallow roots, and it's easy to damage them by raking or digging around them. I would just cut the honeysuckle back repeatedly until it eventually dies.