Kudos to you for wanting to replace these invasive plants with native plants.


Starting with the Japanese honeysuckle (L. japonica) we have 2 native honeysuckles in bush form that would make great replacements: Diervilla lonicera and Lonicera canadensis, both with similar yellow flowers.  If you want to put in a vining native honeysuckle, we have two for this area Lonicera sempervirens (Trumpet honeysuckle) and L. dioica. They both have red flowers and the L. sempervirens is readily available in nurseries.
Japanese honeysuckle spreads rapidly because it contains chemicals (alleopathic) that prevent other plants from growing . The native honeysuckles do not have this chemical and therefore can exist nicely in a layered landscape.

Chinese privet - Native alternatives that are readily available and have tremendous insect & bird benefits include:
Aronia arbutifolia - Red chokeberry
A. melanocarpa - Black chokeberry
Ilex glabra - Inkberry holly (needs male & female for berries)
Myrica pensylvanica - Bayberry
Viburnum prunifolium - Blackhaw viburnumPhysocarpus opifolius - Eastern ninebark

English Ivy - This is an evil spreader and will fairly quickly take over your trees.  Right now, from your photos, it looks like it is just starting to creep up the trunks. I will cover removal later.
Native alternatives that will offer more color, texture & layering opportunities include:
Aster divaricatus - Wood aster
Chrysogonum virginianum - Green & Gold
Dennstaedtia unctilobula - Hay scented fern
Pachysandra procumbens - Allegheny pachysandra
Mitchella repens  - Partridgeberry
Asarum canadense  - Wild ginger
Chimaphila maculata  - Striped wintergreen
Polystichum acrostichoides - Christmas fern
Allium tricoccum - Wild leek
Carex pensylvanica - Pennsylvania sedge (excellent edging for woodlands)

You didn't mention it, but if you have a deer issue, any of the native ferns mentioned above (and there are many more I didn't mention) are all very deer resistant.

Removal of invasives:   If you are completely against the judicious use of herbicides, removal will be more tedious.  I have attached publications that will cover these options.  This would appear to be a good winter for removal of all of these invasives, as it is projected to be fairly mild. English ivy will be the hardest to get rid of, followed by the privet and then the honeysuckle. The ivy will re-root from any piece that has a node or bump on it. To start, in the spring, cut the ones growing up the tree at the base and then treat the cut pieces with a dab of glyphosate (RoundUp is the most common trade name ) applied with a q-tip or sponge brush. You may be able to pull the vines on the trunk off as they are fairly young, but we often encourage them to die back after the herbicide application, as pulling can damage the bark. Following a rain when the ground is soft and not yet frozen, go out and pull out as much ivy as you can, try to get the roots. I have attached a publication that explains all this in detail.

For the privet and honeysuckle, prune out as much growth now as you can and remove so it doesn't reseed.  In the spring further prune the shrubs to a main trunk/stem and then immediately after pruning, paint the stem with glyphosate.  This will need to be done when the plant is actively growing.  So clean up and remove what you can now, then deep prune and treat as spring starts new growth.  By judicious use of glyphosate, I am saying apply directly to the cut using a paint brush, sponge brush, etc. Do not spray. Glyphosate is a systemic herbicide that will go through the vascular system of the plant and only affect the plant it is applied to this way.  Privet & honeysuckle will grow from the roots so you need to kill off the roots so new plants don't sprout up. I have attached a publication discussing the ways to control Chinese privet. From your photos, it looks like yours are fairly small still.

When you clean up the foliage, branches, etc. this winter, you may lose track of where they are, so mark them with a flag to go back and treat with the herbicide in the spring.  Leave enough branch to make a fresh cut in the spring for the herbicide application.

The Sussex County Master Gardeners are having a free workshop that you might be interested in. Registration can be found here:
https://forms.gle/pm3mKi94wZG6y2FQA

Tuesday, February 20, 1 p.m., Landscaping with Native Perennials. Master Gardener Terry Plummer will present. Terry will introduce you to a wide variety of native plant materials, that will draw insects and the birds that love to eat them to your garden. Native perennials will provide a delightful landscape that will make your garden life easier with less watering and less fuss. In-person and Zoom.

If you want to look at great photos of layered native landscapes for ideas, I suggest reading The Living Landscape by Rick Darke & Douglas Talamy. I have borrowed it from the Delaware library system numerous times.

Good luck and feel free to contact us if you have further questions. Thank you for taking these steps to return our environment to a more natural state.
Happy New Year.

You are very welcome and good luck with your project.