Of course it takes time for your voice to get used to a lot of singing, but you can't compare it to running a marathon. You just don't get better by doing it. You get better by knowing what you do, discover mistakes in your technique and directly working on those problems.
If your voice is strained after a few songs, you propably have a problem with your breathing, which is propably the most important aspect in singing. You may feel that you don't push or force the notes, but the fact that your voice starts to crack that fast tells me otherwise.
We could exchange a lot of tipps and how to do it right in theory, but in my opinion you won't get the results you want from a board on the internet. If you really want to sing and don't want to ruin your voice, go get a vocal coach. I know, they cost a lot of money, but it's worth it. The right teacher can help you improve your voice and your overall singing experience a lot, so it's worth the money, even if you are no professional.