This is a common question many people have when they first get into the sport. They work out in Gold's or on campus or somewhere that might have a great set up but lacks stones, yokes, logs, axles, farmers and the rest. You can still get strong and you can still compete even though you're at a clear disadvantage.
First, I need to tell you that the disadvantage is real without the equipment to practice on. Doing yoke or stones is really only like doing yoke or stones. Making up a new exercise or rigging up something in your gym to mimic these lifts will only get you good at the lifts you made up. So, stop wasting your time and just use the gym tools around you to get stronger.
The best thing to do is find someone with the equipment to train on. Go work with them even if it's one weekend a month. You could also just compete and figure things out on the fly and hope that after several contests you will get much better. The latter is a little risky but you will meet more people you can train with and hopefully you're not an asshole and people will let you train with them.
As far as what to do in your gym, here are my suggestions. And let me just add that I have the average trainee in mind, one who has little experience in competition and has really only lifted in a generally traditional environment. For example, if you have experience with Olympic lifting (not doing a bunch of snatches with 95 pounds but can move some serious weight) your path to strongman will be different, but that is a different article. Back to my suggestions:
Press a lot. You need to have a big overhead press because this is coming at least once in every contest. You can keep the strict overhead presses in for shoulder strength and development but you need to be able to jerk or push press. If you haven't done those, take this time to figure them out. You can do these out of the rack or clean the bar from the floor. You can also get some fat gripz which everyone probably has by now and make your bar more like an axle.
Now that you will be overhead pressing a lot, you need to still find the time for the bench press. Either bench press, incline press, or floor press will work but you need the work for your upper body strength, especially for your triceps. Dips are good too.
With all this pressing you need some balance so don't forget to hit rear delts with flyes or face pulls. You also need to work those lats and if you don't do barbell or dumbbell rows you're missing out. These are absolutely essential to having a strong back. With all the things you have to pick up in strongman from stones to kegs to sandbags a strong back is critical.
What is also essential for your back? Deadlifts. You will see all kinds of deadlifts in strongman and you need to be good at all of them since there will usually be some kind of deadlift event in every competition as well. You need to do these heavy from the floor and from 18" but not neglect to work some other heights and angles.
Deadlifts are also going to be good for your grip. Without events, you can probably handle more grip work in your training. Start with reverse curls, hammer curls and wrist curls, then add wrist roller, plate pinches, hub lifts, thick handle lifts, grippers, whatever you can pick up and hold.
And if you're so strong you're ready to test your mettle you are probably already squatting. Back squats are great, but so are front squats. Without implements you will need both. When you do get to use more implements you will likely do more front squatting. Front squats not only save your back for events but they are front loaded as are most events.
Building muscle is also important. You need muscle to move weight. Leg presses, leg extensions, leg curls, straight leg deads, lunges, calf raises, ab wheel, sit-ups, curls, delt raises, dips, pull-ups, etc. you will need muscle so don't leave all these to the bodybuilders.
And finally you need conditioning. Plan on at least two days. If you have no sled or prowler, you're running hills. If you have a battling rope, use it. Preferably you can put sprints the day after legs and rope the day after pressing.
So, a sample week would look like this:
Monday
Push press from rack working up to 3RM, then -50# and max reps
Seated db press
Dips
Pull-ups
Rear delts
Curls
Reverse curls
Wrist roller
Tuesday
Battling rope 12 rounds 20 sec on/40 sec off or concept rower 15 min 20 sec hard/40 sec cruise
Wednesday
Box jumps
Front squat
Leg press
Leg extension
Leg curl
Seated calf raise
Ab wheel
Friday
18" deadlift
Stiff leg deadlift
Bb rows
Bench press
Pressdowns
Plate pinches
Saturday
Hill sprints
I should also mention you need to not neglect your mobility and flexibility. Stretch. Make sure you have good range of motion and that right to left you are not cockeyed. You might need some unilateral work in that case.
If you have questions about why I chose some of the exercises above in particular or about planning out your own training, get in touch.