How do I kill Working Joes with starting weapons?

First and best answer: don't try.

They're extremely tough and they take a lot of whacks from your only early-game weapon, the Maintenance Jack, to bring down, however, their sight ranges are limited and their patrol patterns are, much like the Working Joe itself, simple (though perhaps not brilliantly so). If you're spotted, they can't go in vents (even though they may know you are in there) and don't tend to look under desks if you break line of sight for a bit beforehand.

However, there is an achievement on Steam for doing this, "My Turn Now," which involves killing a Working Joe with only the maintenance jack. Not, "the maintenance jack and a couple gadgets," [even if those gadgets don't do anything to a Working Joe] not, "the maintenance jack and a couple shots from the revolver"; all you are allowed to use is the Maintenance Jack, and it's a bit of a doozy. You will almost certainly get hit doing it and run a serious risk of death, but the best way I've found is to be persistent, pick the right environment, and have lots of materials on hand for medkits.

The right environment is one where you have fairly uninterrupted time to whale on a single Joe without attracting too much attention, plenty of opportunity to sneak up on your Joe and ability to break sight and hide (nearby vents are good for this), and finally and most obviously, one where you don't have to worry about the Alien, because this process is both loud and time-consuming.

It takes about 8 hits, from what I've seen, to down a Joe; way more than you will get in before it retaliates [my maximum "combo" on a wounded Joe was four, and that's only because the third hit staggered him, allowing me to slip in the fourth]. If you sneak up on it, you'll likely get between two and three solid hits in before it attacks you; either be ready to get out of reach or be fast enough on that E key to not take too much damage. Look at your healthbar (and listen for any unwanted company) and decide whether you should stick around or find a place to hide while you heal up. Just keep at it and, eventually, Joe will fall to the floor in a puddle of his own milk and pasta and you'll be left with an achievement as consolation for all those SCJ Injectors you just used.

Well, unfortunately until you get a revolver there really isn't a way to kill them. Even if you sneak behind them and hit them with the bar, it won't do enough damage and then they catch you hand and beat the crap out of you. Once you get the revolver, it is best to shoot them 2 times and then after the immediately second shot hit them with the bar. But with nothing but the bar there's nothing to do. Not even sneaking up behind them and hitting them works because before you kill them they will get you. It is something that is seriously annoying. I would like to at least be able to sneak up on them and go bezerk not giving them a chance to recover, but oh well... Hope this helped.