Training but avoiding / dealing with injury

The best way to handle injuries is not to get them. 

Only partly joking with the above comment.  There a number of things you can do to reduce your chances for developing injuries or mitigating the severity of any you do get.  For example, build into any training program gradually, get a bike fit, have your swim form checked out for obvious flaws that could put unnecessary stress your shoulders, wear appropriate running footwear, etc.  Since most endurance sport injuries are overuse related, these simple things will have a significant effect on cutting your risks.

If you do develop the inevitable muscle ache or pain, treat it quickly.  RICE (rest, ice, compression, elevation) is usually a good place to start and can often short-circuit any developing injury before it becomes chronic.  Rest can include complete abstention from the activity in which you experience the pain or just some moderation in volume and/or intensity until the issue resolves itself.  But if a problem does persist, gets worse or recurs regularly, see an appropriate specialist (often a sports med doc) ASAP.  Don't bother to post your symptoms on the web and practice diagnosis and treatment by internet--at least not without also seeing a specialist in person.

The biggest mistake is trying to train through an issue so you don't fall behind some plan.  The result is usually worsening the condition and ending up with a treatment that involves an even more significant time away from normal training.

Stretching and strength training are often thrown out as useful as well.  Evidence is very mixed and some studies have shown increased injury risks from those as well.  In general, they are more likely to be useful in rehabing an identified issue than "prehabing" some potential unknown issue.  Just be cautious in any general stretching or strength program should you choose to use one (the same way you would be cautious in building your endurance program).

This is my fifth year in the sport (and in each of the individual ones as well) and I have had only one injury that required more than simple RICE.  That one was most certainly caused by building my training load too quickly for my body to adapt.  And all it required to "fix" was essentially a more aggressive RICE treatment (no running for about a month, some targeted stretching and anti-inflammatories, etc.).  Since then, I have tried to solve any potential issues by simply backing off my training a bit and have been fortunate in having that be sufficient to avoid any other major problems.