The sentence that contains the correct word usage of evade versus invade is "Corn leaf aphids invaded the crop and caused damage to the plants." If we replace the word invaded with its definition we can see why. The sentence would read, "Corn leaf aphids entered the crop and caused damage to the plant. This makes sense. A corn leaf aphid is a pest, so it would not make sense if they evaded or left the plant and caused damage. That would be a good thing.
You can use the same technique to see why the other three sentences use the incorrect word.
<u>The thieves were able to invade being arrested by the police. </u>
This would read, "The thieves were able to enter being arrested by the police. This does not make sense. Rather, it should read, "The thieves were able to evade being arrested by the police." Thus, meaning they were able to cleverly escape being arrested.
<u>Guerrilla forces evaded the capital city and announced their power.</u>
This would read, "Guerrilla forces cleverly escaped the capital city and announced their power." While this sentence could make sense in the right context, it is more likely that they forcefully entered the capital city, or invaded it, in order to announce their power.
<u>Sheila tried to evade the private party by bribing the security guard.</u>
This would read, "Sheila tried to cleverly escape the private party by bribing the security guard." Again, this could make sense in the right context, but it is most likely that she bribed the security guard in order to enter a party that she wanted to intend. Therefore, the use of "invade" makes more sense.
