Are there any differences between "My heart beat wildly" and "My heart beat strongly"?
Yes, although there may be situations in which some native speakers would use them more or less interchangeably, these two phrases have different nuances. If I say that "my heart beat strongly," I am probably giving a neutral or mildly positive description of my physical state; I may also be implying that I was in a positive mental or emotional state. For example,
My heart beat strongly as I neared the halfway point in the marathon.
My heart beat strongly as the national anthem played in honor of our victorious Olympic athletes.
On the other hand, saying "my heart beat wildly" suggests that my heartbeat was very fast and possibly irregular. Additionally, there is likely to be an implication that I was excited, frightened, upset, or physically ill.
My heart beat wildly as the horse galloped faster and faster.
suggests that I was excited or frightened, depending on the broader context.
As soon as I had swallowed the drink, I knew something wasn't right: My vision blurred, my mouth went dry, and my heart beat wildly.
suggests heart palpitations. One would be very unlikely to use "my heart beat strongly" in a sentence like this, since "strongly" implies vigorous good health.