I'll answer in English, since I assume your native language is English and some nuance of my answer might be lost if it was in Japanese. Messages on this board are mostly in English as well, with a few exceptions.
Yes, there are many cases where particles can be omitted in conversation. For example, は and を are frequently omitted:
Notice that the は is often replaced by a comma, which in speech means a short pause. Also if the は is used to emphasize the fact that "X" does but "Y" does not, then it is much less likely to be omitted.
I think the first は can probably be safely omitted, but the second one should be kept. This is because that は emphasizes "I hate it, but other people may not".
Other particles like に can be omitted as well.
の can also be omitted sometimes when it is used to connect nouns. For example:
I think the latter (the one with の omitted) is more often used in titles (like 東京大学)
This is just a small sample of places where particles can be omitted.
On the other hand, there are some cases where particles would not normally be omitted, like で in this example:
Removing で would yield "バス行ったよ", which sounds like "the bus went", instead of "I went via bus".
Here, I think it would be awkward to remove に (though the meaning could still be guessed):
In this example, it would sound odd to remove の because it changes the meaning of the sentence:
Without the の we end up ”僕を返して", which is "give me back" as opposed to "give mine back!"
I think omitting particles is much like omitting subjects, in the sense that it takes a certain amount of intuition, or feel about what is appropriate and what isn't. In other words, there is no hard and fast rule.
I would say for most beginning/mid-level students it's best to err on the side of including particles, and then gradually start dropping them as you see them dropped by native speakers.