"Woke" originally meant "aware of and well-informed about systemic social issues affecting everyday people". Conservatives have co-opted this word and use it to describe anything associated with leftism or social liberalism. It is intended to be negative in that context.
"DEI" stands for "diversity, equity, and inclusion". It refers to policies that intentionally include people of diverse or minority backgrounds in the context of employment or political appointment. Conservatives use it to describe (in their view) hiring practices that select less-qualified candidates of these backgrounds against the favour of those who may be more qualified. In that usage, a "DEI hire" or "diversity hire" is a person hired or appointed solely on the basis of their race, gender, or some other status as a minority even though they are not qualified for the role.
DEI hire is actually supposed to be “if you have a choice between two candidates who are equally qualified, you choose the one which adds diversity to your team”. There’s nothing in DEI hire about choosing the less qualified person. If anything, from what I’ve seen people who are non-white usually have more degrees and qualifications than their white colleagues. I mean, look at Kamala Harris vs. Donald Trump right now…
That's true in reality, but in the minds of those who use it to diminish people, the implication is that race was the deciding factor - because of course, to them, only whites are competent, so there's no other reason anyone else could have been chosen.
I was once heard of a team where two equally, incredibly talented candidates were options. One of them had the same name as two other people on the team so they picked the other guy. Can't have three John's ya know?
(The name wasn't John, it was a fairly uncommon name, which made it waaaaay funnier)
Conservatives use “woke” to mean the same thing leftists mean when they say “redpilled”: edgy people roleplaying enlightenment instead of actually seeking it.