Learn English – How to say I fulfill the requirements with the word “satisfy”

• I will arrive there at about 8 o'clock or a little later (i.e. at 8:05 or 8:15...)
• I have read about 10 books on Chinese history or a few more (i.e. maybe 11 or 12, I'm not sure).
• She looks 40 years old or a little older (i.e. maybe 42-43).

Both 'or so' and '-odd' can mean either a little more or a little less. If you want the number X to be understood to be the smallest approximate number, you might use "at least X" or "X or more" or "more than X".

• I won't make it there before 8 o'clock. I will probably be 10 or so minutes late.

If you are certain you won't arrive before 8 o'clock, you should say so directly. Otherwise, we would just say "around 8 o'clock, but I might be a little late." with the understanding that if we are lucky and don't have to stop at too many traffic lights, we might show up at 7:55.

• I have read more than 10 books on Chinese history.

If the number were much higher than 10, we would expect you to say "I have read more than 40 books." or "I have read about 100 books on Chinese history."

• She looks at least 40 years old.

Similar to the second example, if you thought she could be a lot older than 40, you might say "She looks around 50 years old." meaning maybe 48 or maybe 52.

I personally find the -odd suffix difficult to use. It always seems better to me to say "about 5 things" instead of "5-odd things". Usually I don't use it with a specific number. I might say for example,

"That sandwich has been in the fridge for a week and some-odd days - throw it away!"

That would mean it has been at least a week and a few days more. If I hear other folks use it in conversation, it doesn't strange to me at all, so don't think I'm telling you not to use the -odd suffix. I would just take someone else's advice on how to use it naturally in your examples.

My question is: is it common to say "I can't seem to do it" when one really means "It seems I can't do it", and is it "correct" (in whatever sense that makes sense)?

Yes, it's common, and the difference is that the first expresses a certain level of frustration, as in, "I've looked everywhere and I can't seem to find it."

The second construction would express a certain level of resignation, "It seems I can't find it, so we'll have to do without it."

The two can also be used interchangeably when the level of either frustration or resignation is low.