Sonic does have his down smash and forward smash that may act as his kill moves....
Here's some advice that can hopefully help you.
When approaching most characters, use the side-b. Personally, I like to open with a down-b then it comes down to whether I wanna fake them with a jump cancel into a homing attack or just follow through with my down-b then home attack. Another great approach is your fair. Mainly against characters taller and/or bigger than Sonic, it works very well, especially if you fast fall and follow up with 1 or 2 more fairs. Btw, make sure your fairs are shorthopped. Against more experienced players, you'll may want to lay off the side-b and use some fakes. Since wavedashing has been cut, you're able to dash cancel with or without the shield (without the shield makes it less obvious IMO). And dash dancing to me has lost its effectiveness.
Remember to always stick to your guy, and keep harassing him. Obviously you'll use your better judgment when and when not to stick to your opponent, but its key to keep your spacing and know when to not let him/her breathe. Your spring jump can be used as an offensive technique. Jump above the opponent, spring jump and use down-a to fast fall right back down with no lag. Your opponent will probably wait for you to come back down to attack, but you have plenty of options on avoiding. Sidestepping, and punishing his mistimed attack can help. Also, many people say Sonic's neutral-a sucks. I beg to differ. Sonic's neutral-a sucks damage wise, but just like Sonic's down smash, if you want people to get off you fast, its great. Like if you're having an aerial battle and your opponent gets to the ground before you, and all you have are attacks that leave you open thanks to lag, use your neutral-a. Dont worry about it not racking up %s, worry about using it to get people off you and give you space as you land.
When your opponent is down, I recommend using either the side-b, or a running charged up-smash, or maybe even your running dash. With the side-b, follow through, and hit them with your uair. If they're at a really high percentage, follow up from that uair with a spring jump uair or at low percentages, you can follow with a homing attack.
Now for (h)edgehogging, I like using homing attacks. Run off the stage, fast fall enough to be below your opponent, and use it. What you can also do is use the spring from your 3rd jump to gimp someone from coming back to the stage. I like using the spring for characters that can fly, but ill let you decide whats best. If a character has a low percentage, dont bother using the homing attack. Maybe your spring. At low percentages I like to chase them with another side-b into an uair, or if you're lucky enough, fair.
One of the characters ive found to be near helpless to Sonic's (h)edgehogging is Ike. Chase Ike, use your spring board at the same level as the edge of the stage and watch that spring bounce him farther from the edge.
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