I know the concept of whether one needs an EF or not is often debated here. But, in your situation I think some sort of EF would be warranted. How much? It depends on how steady you think your jobs are, generally how is your health, how is the health of your vehicles, do you have pets/kids, etc.? At a minimum you should have enough to cover life’s emergencies (car repair, flights for death in the family, etc.). If you think your job might be in jeopardy, then you’ll want to have a very robust EF.
Also, once you decide on how much you need in your EF, you don’t necessarily have to fund it overnight, it can be funded over the next 3-6 months (assuming your job is steady). This way you can still feel good/motivated about moving closer to your debt reduction goals, but adding in a little protection along the way. This is a matter of risk tolerance.
And I agree with the general consensus of some sort of EF, pay IRS ASAP, then pay SL aggressively after that. You need to get the monkeys off your back.