Japanese language can be quite a challenge when it comes to colloquial speech. Just as we (Japanese people) are fond of anything "minimal" things, this is seen in the language as well. It is always wise and best to learn the correct sentence-structuring if you're a beginner learner. Just like Japanese learn the correct grammar of English, or any other language.
Also, remember that unlike English, Japanese has many levels of speech - that is, the casual, formal, ultra-formal, humble...to name a few. While the formal and other respectful speech commonly follow the correct sentence-structure - SUBJECT - OBJECT -VERB, the colloquial-casual way is a bit confusing. First, the pronouns may be dropped - then some particles may be dropped - in short, whatever is understood by both speaker and listener is cut off and you end up with short, one verb sentences like. *Iku!* (Which can mean "I go" "He/She goes""They go")
May you keep enjoying Japanese! :D