I was recently deported from the United States. I overstayed there without a visa for a long period of time, I was arrested last year and charged with 6 felonies but all my charges ended up getting dismissed & i was not convicted of anything, but due to my immigration status i was deported back to my home country. I would like to know if i am admissible to travel to Spain? I have a family member that lives in Barcelona and offered me to go stay with her. I have a Honduras passport and have read that it is not necessary to have a visa to travel to Spain for honduran citizens.
As a Honduras citizen, you don't need a visa to enter any country of the Schengen area, including Spain. You can stay for a max of 90 days, following the 90/180 rules.
The principal problem you might encounter is that, with a overstay in your historial, and being invited by a familiar to stay with her, the officer at the immigration interview might see you as likely to overstay again, and might deny you entry. To get a better chance of entering, you should bring evidence of strong ties to your country, a good financial situation, and a return ticket.
If, on the other hand, you're planning to stay longer, you'll have to get a residence permit. For that, you need to show that you have no criminal records for 5 years in your previous countries of citizenship, but this shouldn't be a problem, as you were not actually convicted. Note that there are other requisites, and this might not be an easy path even if possible.
Finally, let me echo user90371's comment: if you get asked about your immigration history, tell the officer the truth. Getting caught lying will probably lead to a ban, and many complications in the future.