What you're looking for are strength or fitness standards. Generally these fall into two broad groups:
- Strength-biased evaluations, which will generally look at things like your back squat, deadlift, bench and overhead press, and maybe chin-ups. Many examples of this will delve into evaluating power or athleticism by including exercises like the Olympic lifts (e.g. the power clean) or vertical jump. See the Starting Strength Standards (PDF).
- General physical preparedness evaluations (which are not as focused on strength), which will include all of the above as well as feats like kettlebell work, pistols, handstands, muscle-ups, mile run times, 100m dash times, 2000m row times, and so on. They can get quite extensive. CrossFit Seattle's Athletic Skill Levels is a good example.
The benefit of the first approach is that it's simple. If your basic lifts aren't wildly out of proportion, then you can be confident that you don't have any major areas lagging. The drawback is that its evaluation is confined to strength in major movements, which can lead trainees into "teaching to the test". For example, the back squat is a good metric, but one should also be able to front squat and do heavy lunges. The trap is becoming overspecialized.
The benefit of the second approach is that it's comprehensive. It covers many different aspects of fitness (conditioning, strength, mobility...) and many variations of similar movements (e.g. dips, push-ups, military press). The drawback is that it's quite a wide variety of skills, which can diffuse the effectiveness of one's training. Having so many goals is often counterproductive. The trap is chasing too many rabbits.
If you're just concerned with strength for basic tasks, then I recommend getting beyond the "novice" level with some kind of deep squat (front or back), a deadlift, and some kind of pushing and pulling (e.g. dips and pull-ups), then chasing some of the items from GPP lists like the Athletic Skill Levels.
To get a more specific evaluation than these too approaches would require a personal evaluation by a trainer or coach.