I am in the 7th semester of my engineering. Can I apply for companies on an off-campus drive? What are all companies I can choose from?

Yes you can apply if your college allows means some college does not allow their student to sit in open campus as it spoils the repo of college but if your college cannot invite the companies for placement then you can definitely sit and get placed in companies
If you are from cs/it branch then you will have many opportunities, just focus on your skills and project and then go for the placement. You can sit in mass recruiter like TCS , Accenture, Wipro , Infosys as well as tech giant companies like Snapdeal , Flipkart , Amazon, Barclays and many more . For Mech branch doors are always open you can go to both software field and core field so choose wisely. Electronic communication student can also go to software field if they are comfortable with it but the first question will be that why they are changing their steam so be prepare for that . EI student can also get placed if they are good in communication and having luck .
Hope this helped you.