You're in luck, since I've been doing a fair amount of work on Publius Clodius for my thesis. This is a pretty broad question but I'll see what I can do for you

There's no doubt that in the wake of Publius Clodius' election to the tribunate he exercised enormous influence in the city. He was no Pompey or Caesar, and Jeffrey Tatum argues pretty persuasively that he was certainly not as revolutionary as Cicero makes him seem, but there's no denying that Publius Clodius exercised an influence far in excess of his actual political standing. The most obvious indication of Clodius' influence is of course his popularity, which was not at all limited to the urban poor. There's a great deal of confusion surrounding Clodius' gangs (and I don't really agree with Tatum's assessment of them), but alongside such insulting phrases as dilectus servorum Cicero also mentions the tabernarii, shopkeepers, as participating in Clodian demonstrations. Clodius' popularity among the plebs was high enough that when he was murdered there were more or less spontaneous riots throughout the city, including the famous one that burned the Curia.

Clodius also understood that the favor plebis was not enough to secure passage of laws and election to magistracies. The comitia centuriata heavily favored the wealthy at the ballot, so any politician hoping for higher magistracy had to court the favor of the nobiles and the wealthy and secure the personal connections among them that were necessary to succeed at politics. In this Publius Clodius, though young, was lucky, since he was born into the Pulcher line of the Claudians and never entirely lost the reputation of his family. Still, even in 58 he was able to maintain friendly relations with the nobiles that would be of great support to him later. Tatum shows that the leges Clodiae were a relatively mixed bag of laws, with the most notable (the leges de collegiis and de frumentaria) being decidedly populist while, for example, the lex de censoria notatione can only be reasonably interpreted, if we reject the idea that it was passed purely to protect Clodius personally from censorial ejection from the senate, as a limit on the powers of the censors on behalf of the senatorial class, which was increasingly showing dissatisfaction with the arbitrary and one-sided nature of censorial reviews. Clodius maintained excellent relations with Cato, whose appointment to Cyprus was simultaneously a convenient way to keep him from interfering and an expression of tacit approval on the part of the boni--Clodius' later opposition to Pompey met with fairly widespread senatorial support, even if naturally this support came and went during particular issues (as was usual for Roman politics, though Clodius' failure to prevent Cicero's recall must've been a rather shocking defeat for him, given the senatorial support Cicero's exile had enjoyed only a few months earlier).

The thing about Publius Clodius, though, is that he really had very little lasting impact on much of anything. He was murdered in 52 before he had held any magistracy higher than the aedileship, and his laws and political relationships were largely maintained during the course of his career by careful relationships with the senate and his own obstruction of any attempt to remove them--they therefore depended in large part on his own personal influence. With the exception of the lex de frumentaria, which was the first of a long series of very free grain laws, none of his laws had much lasting effect following the civil war. Most importantly the provisions of the lex de collegiis were mostly knocked down by Caesar, who outlawed all collegia without an ancient pedigree, which would include Clodius' new collegia and the ones that he had revived after Sulla's ban. His personal relationships with the nobiles naturally did not outlive him, and Clodius' own personal arrogance, which was an outward sign of his influence, didn't either. Publius Clodius was by no means on the level of the triumvirs, though he was not merely a tool of theirs, but Clodius often arrogantly overestimated his own standing. In 58, when he attacked Pompey and then Caesar, he made a serious error, and was completely routed by Pompey, though he managed to recover and continue his attacks. Publius Clodius was no political mastermind, though he was almost as effective a politician as he liked to believe himself to be, but one thing that's indisputable is that he indirectly introduced a form of politics that dominated the 50s, probably the most politically turbulent decade in Roman history. Tatum argues that Publius Clodius transformed the way that a popularis used the support of the plebs. Up until Clodius favor plebis had largely manifested itself in electoral success and plebiscites. Under Clodius the urban plebs begin turning out for mass, relatively organized, demonstrations and opening into gang violence. Tatum argues that under Clodius "the plebs urbana developed a sense, however inchoate, of political identity and of political entitlement" that hadn't really been there before--in a surviving speech of Gaius Gracchus (if genuine) the great statesman admits before the urban plebs that no one appeals to the people unless he wants to get something out of them, not necessarily to champion their interests. This cannot have been an intentional consequence of Clodius' legislation, but it's an interesting one, and one that had lasting impact on the 50s. Throughout the 50s both Clodius and his enemies--most notably Pompey, who organized his own gangs, and Cicero, who operated through Milo--fought in the streets of Rome and staged disturbances and riots on a massive scale, something that had never been seen before.

Even then, though, that's largely a phenomenon on the 50s. Large-scale urban violence persisted in the years following, particularly in the wake of Caesar's murder, but the sort of thing that you see under Clodius seems to have been effectively prohibited, though I'd argue that we definitely see the urban plebs flexing its sense of political entitlement well after Caesar's death. How much Clodius can be said to really be the originator of this situation and how much he really just enabled something accidentally that had been cooking for some time I don't think we can say reliably. But if you want a short version to the question of how influential Publius Clodius was, then I'd say that he was of enormous, even pre-eminent importance (though he never eclipsed Caesar and Crassus or, most notably, Pompey--though not for want of trying) during the few years of his greatest power. But his actions really had little importance in the years following his death (not even his attempt to drive Pompey away from politics, which might have caused a rupture between the triumvirs--at the Conference at Luca Publius Clodius and Pompey became firm allies) and he was of relatively little importance to the triumvirs (at least after Luca) and had little lasting impact that would last into the Principate--what impact he did have was mostly indirect. Amusingly, one of Clodius' more influential direct actions that would have repercussions on a scale much greater than most of his legislation was actually his death, since the riots that broke out in its wake were the important factor in Pompey's nomination as sole consul.