How do I tell the difference between the native and invasive...

1. ...Phragmites?

See "Phragmites: Common Reed - Morphological differences between native and introduced genotypes" at Cornell's Biological Control Program

2. ...native American bittersweet vine Celastrus scandens and the invasive exotic oriental bittersweet C. orbiculatus?

"Using fruit and leaf characters, the two species can be discriminated from each other. However, certain traits are more reliable for correct identification than others. Classically, the position of the fruit and flowers on the stems has been cited as the most definitive means of discriminating between the species. Oriental bittersweet has fruit and flowers located in the leaf axils along the length of the stem. American bittersweet, however, only has fruit and flowers in terminal clusters. There is also a difference in the color of the capsules surrounding the ripened fruit in the fall. Oriental bittersweet has yellow capsules, while those of American bittersweet are orange. Another difference in color is the pollen color of the male flowers. The pollen of oriental bittersweet is white while that of American bittersweet is yellow..." - American and Oriental Bittersweet Identification - the US Geological Service's Great Lakes Centre

Note: along a couple southwestern Ontario roadsides, I found both species side by side + the hybrid species of the two. So I couldn't even seed collect from the native species, because of the possibility the flowers had been cross-pollinated / its seeds would be hybrids.

3. ...native eastern Wahoo Euonymus atropurpurea vs. the invasive exotic winged burning bush E. alata, climbing euonymus E. fortunei and spindle tree E. europaea?

Unfortunately, around here, it's probably the exotic -- I haven't stumbled by the real thing yet -- still to be sure (and you have to be because there are a few out there + some native plant nurseries sell them = some one's planting them some where) the best native vs invasive euonymus ID advice I've found is on page 123 of “Growing Trees from Seed - A Practical Guide to Growing Native Trees, Vines and Shrubs" by Henry Kock with Paul Aird, John Ambrose and Gerald Waldron:

European spindle tree E. europaea [exotic]: the identification of this close relative of E. atropurpurea can only be made with certainty at flowering time. The European species has greenish white flowers in late May as compared to the maroon flowers (in June) of the native wahoo. The European spindle tree holds its leaves much longer into the fall, and the twigs tend to be thicker and more rigid than wahoo. However, due to variability in both species, the two are occasionally so similar vegetatively (including the root sprouting) that without knowledge of the flowers, the nearly identical fruit should be left alone – or the flower colour should be verified in late May.

Winged burning bush E. alata [exotic]: A dense, outward-arching bush originating in Japan. It has small orange fruits on short stems that persist into the winter. Twigs on this species are prominently four winged, a characteristic that is more diminutive on a more compact-growing horticultural cultivar but still gives this species a distinctly square-stemmed appearance.

...[Besides these] two 'ornamental' deciduous shrubs that ...have become naturalized (extensively in many places) in close proximity to older settlements and parks ...garden escapees of the evergreen-leaved Euonymus fortunei [exotic climbing euonymus aka wintercreeper] are also beginning to find their way into the wild."